no half-heartedness and no worldly fear

All throughout season 1, Galadriel's one and only drive and motivation is Sauron--who, iirc, she'd never had a direct encounter with (if this is incorrect tho, let me know) despite his contributing to causing her much loss and emotional damage. This single-minded determination to achieve her vengeance against and eradicate him, at any cost, can be seen as a period of animus-possession. Especially because, by this point, she'd lost all support for her cause and was very much in "Fine, I'll do it myself!" mode.

"In the course of one’s development, the Anima is likely to possess the man at times and the Animus will possess the woman. [...] An Animus-possessed woman becomes obsessed with power that can manifest as 'social justice' or some other ideology. A woman possessed by the Animus can not be reasoned with" (Scott Jeffrey, 'Carl Jung’s Theory of Anima and Animus: A Detailed Primer of These Two Powerful Archetypes').

It had been so long since Sauron was seen or heard from that Gil-galad, Elrond, the Elven soldiers, everyone wanted to take the peacetime at face value and saw no need to continuing preemptively searching. But for Galadriel, "The animus contributes to her unrest so that she is never satisfied" (M. von Franz, Interpretation of Fairy Tales).

"...we never actually see 'Sauron' for the majority of the season, as we mostly experience the idea of him through Galadriel. For the first season, Galadriel’s defining character motivation is her relentless quest to find and crush Sauron. I wanted the score to suggest that her thoughts of Sauron are always on her mind, always influencing her decisions" (B. McCreary, Scoring Episode 101 "A Shadow of the Past").

"In women, a negative Animus may manifest as...ruthlessness--

--and an unyielding need to be right" (Bay Area CBT Center, 'Exploring Anima and Animus: Jungian Archetypes'). Aaaaand Galadriel was technically right. And she knew she was right. But she didn't have a way to prove it. Besides accomplishing the goal, finding Sauron himself. And of course her animus was negative, she was angry, traumatized, hurt, and no one wanted to hear it anymore, even her best friend. They were like, How about you just go, and be done with all this. But easier said than done. She basically indicated that the darkness was within her heart (foreshadowing??), so no, it's not something she could've just set down to go about frolicking in Elven Heaven. "[L]etting it lie, is not an option."

So she remained obsessed with hunting Sauron, with destroying Sauron, with Sauron. So deep, intense, and all-encompassing was her (animus's) singular focus on this one being, that it's like she narratively conjured him up out of thin air. Out in the middle of the ocean, of all places. She hopped off a boat, and there he was--her Animus, externalized and embodied just for her. The irony being, after all o' dat...she didn't realize it was Sauron--because he was Halbrand, a Southlander human, probably the most innocuous humanoid form in Middle-earth. Even Galadriel's subconscious wouldn't immediately recognize this person as its animus projected into the world.

But he definitely is. As we know, there's a trait of TRoP-era Galadriel that's character-defining in Tolkien written canon, but so far is not present (at face value) in the show--her hunger for power, leadership authority, and dominion in M-e. As highlighted by philosopher K. Wilber in A Brief History of Everything, "the masculine seeks autonomy" (S.J.).

"like her brother Finrod [who could be viewed as her externalized animus of her childhood]…she had dreams of far lands and dominions that might be her own to order as she would without tutelage" "...all that she had desired in her youth…the Ring of Power and the dominion of Middle-earth of which she had dreamed" (The Peoples of Middle-earth)

Now of course, I don't know what went into this story and character decision, why the showrunners went this way, but it's what they did. And what we now know they did is, they conflated that aspect of written canon!Galadriel into TroP!Galadriel's dynamic with Halbrand/Sauron. Which is interesting, considering one of Jung's descriptions of the Animus is a "psychopomp, a mediator between the conscious and the unconscious and a personification of the latter" (Aion: Researches into the Phenomenology of the Self) + J.D. Payne saying that Gal has a "push and pull relationship to Sauron, [who] is basically The Ring personified" (x). So... TRoP!Sauron = The One Ring/power = what written canon!Galadriel wants = TRoP!Galadriel wants TRoP!Sauron. And as I reiterated above, she's wanted him since the beginning, it was the whole catalyst for her s1 storyline. But the type of want developed throughout the season, thanks to Halbrand/repentant Mairon, and Gal's own inner animus projections/delusions.

"...we said, 'How could you have a relationship between the Dark Lord and Galadriel...in a way that was good...?' [H]e has this desire to heal the world, and she has this sort of heroic desire to fix the world also, and so if you could put them in parallel to each other without exactly her knowing who he was, there was an opportunity there." "The chance meetings are preordained in Middle-earth and...what if Sauron is in a place where he's sort of repentant and lost and Galadriel is in a place where she's desperate and obsessed with a meeting?" (J.D. Payne, Patrick McKay, Radio Times/Games Radar)

"Perhaps the best way to understand the nature of Anima/Animus is through the experience of 'falling in love.' [I]t’s both intoxicating and shocking. x

All prior rules fall away. The lovers feel like they can’t exist without each other. x x

"...it keeps him going in a way, her existence." (C. Vickers, Collider)

They think about each other constantly and can’t bear to be apart for long. x x

"our characters have been talking about…and obsessing over each other for all this season," "so...when they do...meet each other, they are weirdly aligned in the desire for this confrontation"; "They're both very hungry for it" (M. Clark, Gold Derby/Collider/AwardsRadar).

In the eyes of the lover, their mate represents perfection" (S.J.). x x

But of course, perfection doesn't actually exist. These new love phase, googly-eyed perceptions of "perfection" are often the result of:

"In romantic love, individuals often project their Anima or Animus onto their partners, expecting them to embody these idealized images. This can lead to falling in love with an illusion" (BACC). "...with anima/animus the projection is in a rather more idealized form: one looks for the reflection of one’s anima or animus in a potential mate" (The Jungian Confrerie)

And s1 Galadriel was soooo guilty of this. Not to say she didn't genuinely bond with the core of Mairon/Halbrand, including his inner darkness she felt related to her own (otp: touch the darkness!). -- "The allure that the romantic partner has at first is essentially the allure of the anima or animus inside the psyche of the lover" (M.K.). -- Plus, anima and animus "are easily projected to the potential partners we are unconsciously attracted to" (K. Melik-Akhazarova, International Association for Analytical Psychology). x

As this scene--and "heavy breathing" on the captions--can attest, she was already physically attracted to/aroused by him (like, why else would she be breathing heavily? She hadn't run a marathon, she was just standing there). In any event, her inherent connection to and compulsion towards Halbrand was real. But she also projected a whole fairytale narrative onto him. In order to fit her own needs and get what she wanted--leverage (which is a form of power). But also, ultimately, him.

"She so wanted to fulfill her vengeance that she made Halbrand whoever she wanted him to be. She...would believe things easily if they aligned with what she wanted. [...] There was barely anything saying that he was the king of the Southlands. He always said he wasn't. But it suited her because she needed to go to Middle-earth and she needed the Numenorians" (M. Clark, Inverse).

In Halbrand, she created a figure to embody the kind of power, leverage, and influence she needed but didn't have on her own at this point. I mean, she tried, but it got her nowhere but arrested. @izalith-witch pointed out that when Galadriel confronted Halbrand with lines like, "you chafe under the rags of the common. And the armor that ought to rest upon your shoulders, weighs upon your soul," she was projecting and subtextually/subconsciously talking about herself. Well, yes! And in the event of such projection, "our partner becomes...an actor cast to play out the role of our anima or animus" (M.K.).

"It was entirely of your choosing. Sauron…making himself out to be exactly what you needed–‘The Lost King’ who could ride you to victory" (Elrond, using extremely apropos wording).

Gal needed "The Lost King of The Southlands" to embody leverage and influence, but also righteous heroism. She deemed herself a hero and savior, and had been channeling all of her animus energy into hunting Sauron--outwardly, in the cause of protecting M-e (internally, in the cause of revenge and "coping" with her trauma and pain). And what could legitimize her plea more than a last scion of a lost royal lineage reemerging to save his land and people--and by extension, all M-e--from the imminently lurking threat of the Dark Lord? It's the stuff of fairy tales. And "Fairy tales frequently portray the Animus as a heroic figure, representing strength and protection" (BACC).

While I love how she was all "free my man, he did it, but also he's innocent"...girl, what the hell are you talking about? She completely made this up. She wasn't there, and had no idea how that fight went down or why. But this is the story she was spinning. This is the archetypal Romantic antihero she was making Halbrand into, in her mind (and to her benefit). And becoming more attracted to by the hour. It was like two birds with one stone because, yes, "Lost and Returned King Halbrand" was the powerfully heroic leader she saw herself as but wasn't being taken seriously as, as well as her key to getting to M-e with an army. But also, she made him even more attractive to herself, and closer to her level--He's not just a regular ol' human, he's royalty! (the dramatic irony being that he's neither)

"The woman is often overwhelmed and shocked by the recognition of her Animus" (S.J.).

"...what she sees as a hopeless mortal that she found stranded at sea has forever changed her. It was really fun exploring how vulnerable this mythical being Galadriel could be. [B]oth of us felt that looking at each other would even be just too intense. [W]hatever they’re feeling is too much" (M. Clark, TVLine).

By this point, she's more than just attracted to Halbrand. She's more than just using him for her agenda. By this point, he's emotionally exposed and touched parts of her that no one else has (or even knows exist).

"If she sees that she has a godlike element within, the result is exhilarating, much like a peak experience. She is now in great danger of 'falling in love with himself'" (R.A. Johnson, She: Understanding Feminine Psychology). "'Peak experience' is a term humanistic psychologist A. Maslow used to describe a higher state of consciousness when…perform[ing] at their best" (S.J., 'Peak Experience: A Definitive Guide with Insights from Maslow & Others') "[S]he felt powerful in a particular way when she was with [Halbrand]" (M. Clark, Nerds of Color)

So, apparently, not just when they were joined in battle together in the Southlands, but her whole experience with Halbrand was a peak experience for her. Which makes total sense because:

One's Animus is the "spirit of inner truth in women" (B. Hannah, The Animus). "The Animus is the gatekeeper to the genuine spiritual life of a woman." "Maslow believed that when having a peak experience, we are closest to our authentic selves—our true identities" (S.J.). "Her time with Halbrand was a time where she was very much herself in some ways[.] So he knows a part of her that other[s] don't" (M. Clark, Collider).

And this is why when he told her, about that feeling of being powerful and in sync together, that he wanted to hold onto it, it keep with him always, and bind it to his very being, she was like, Same. She'd never felt that before, she doesn't have that with anyone else. Because no one gets her, the deepest parts of her, like he does. Especially that--in the show--unconscious "part of her" that craves power, rulership, and the glorious reverence that comes with it. It's more than "I know your mind", he knows her subconscious mind. Because he is the very embodiment of it. "[H]e sees you. Not just who you are, but who you wish to be." And so, in this symbolic role, he very much wants to fulfill the desires of her inner animus. He wouldn't keep saying stuff to her like, "I would've placed a crown upon your head. I would never have rested until all Middle-earth had been brought to its knees to worship the light of its Queen," if he didn't intimately know the part of her that wants that (plus, she started it). This is why he was matter of fact about telling her he sees no difference between saving and ruling M-e/that it needs to be ruled to be saved--he knows she wants to save M-e, and he knows she wants to rule on M-e. So there you go, two-for-one.

Also, the way the "worship the light of its queen" line sounds like something that should be on a Valentine's card. All part and parcel of TRoP's metaphor of Sauron = Power. While Galadriel desires the latter unconsciously/subtextually, she desires the former consciously/textually ("heavy breathing"). It's why his offer of queenship and co-rule of M-e is intertwined with, basically, a marriage proposal. He knows she wants power and dominion -- "That’s his pitch. 'If you and me do this together...I'll give you the power that nobody wants to give you'" (Patrick McKay, Vanity Fair) -- and he also knows she wants him -- "...he knew the feelings Galadriel had for him. [...] Galadriel obviously was in love with Halbrand. She was very attracted to him. [...] Sauron knows this because he gets into her head" (Charlotte Brändström/Haladriel shipper extraordinaire, Nerdist).

Now, this would be all well and good if not for the practically Shakespearean caveat of who Halbrand actually is. It's all very "Too early seen unknown, and known too late. Prodigious birth of love it is to me, that I must love a loathed enemy." But what's partly to blame is Galadriel's own willful projection delusions. She developed deep feelings for the true aspects of Mairon/Halbrand that he revealed to her -- "he genuinely really connected with her, and was genuinely open and vulnerable with her because she understood him on a level that no one had for hundreds of years" (C. Vickers, Awards Buzz). But she also held "The Lost King of the Southlands", a character she created, a fiction, on such a pedestal. Well, anima/animus projections don't last--

"...resulting in disappointment and conflict" (BACC). "...the honeymoon phase in relationships ends once the couple fails to maintain the projections of their partner’s anima/animus figures" (M.K.). "...the difficulty arrives at the moment when the projections lessen and fall, and the individuals are re-seen in the light of reality" (K.M-A.) "It is only when the mirage of the projection is broken up that they will realize how they have been duped" (TJC).

Duped mostly by their own self. My favorite part of the pre-proposal confrontation is that almost rapid-fire back-and-forth they have where he pushes back at her with the truth or more complete truth of her projections and accusations, as she's in the process of processing the dots she's finally connected.

G: "There is no King of the South lands. The line was broken. The last man to bear your crest died over a thousand years ago. He had no heir." H: "I told you I found it on a dead man." G: "No. No, on the raft, you saved me…" H: "On the raft, you saved me." [they saved each other :)]

"He saved her, and she saved him. So they are bound...and I feel that what would make an unbreakable bond is saving each other’s lives" (M. Clark, Inverse).

G: "You convinced Míriel to save the Men of Middle-earth." H: "You convinced her. I wanted to remain in Númenor." [this one especially tells you how hard she was projecting] G: "You fought beside me." [their shared peak, peak experience] H: "Against your enemy. And mine."

Now this one here really had me like !!! when I saw it: "When animus and anima meet, the animus draws [its] sword of power and the anima ejects [its] poison of illusion and seduction" (S.J.). x x x x

[As her previous externalized animus, and as @neyafromfrance95 has pointed out, it seems like Gal's replaced Finrod with Halbrand/Sauron in a certain way. So, through that lens, and hilarious incestuous subtext aside, Sauron-as-Finrod makes total symbolic sense.]

"The outcome need not always be negative, since the two are equally likely to fall in love" (C. Jung, A:RPS). However, in Saurondriel's case, both these confrontations have negative outcomes, because as lovers-to-enemies, this isn't an arc (or, not a straight-line arc) of symbolic Anima/Animus integration, but more like the reverse. They were already in love.

As the key to/revealer of a woman's deep inner life and truth, her Animus "can seem so powerful and god-like that her conscious ego feels worthless and helpless by comparison" (S.J.). x x

And if there's one thing Galadriel absolutely cannot stand, its feeling helpless (/powerless). She'll immediately act to push against or overcome that feeling/position. So, after their "Alloyed" confrontation, she attempts to reclaim her sense of control by...doing exactly what Sauron told her to do--deceiving her fellow Elves and "let[ting] the work proceed" on the Elven Rings. Now, this seems highly contradictory, and, of course, she caught plenty of grief for it in the next season. But I think I worked out, at least on a symbolic level, how she made it make sense.

In true Galadriel fashion, she was very "forgiveness instead of permission" about this (and not even forgiveness, because she was never sorry about it). At least regarding the Elves. Because maybe, subconsciously, she felt she was receiving "permission" from her Animus to get what she wanted anyway. The Rings are a form of power, her unconscious motivation. She later claimed she had to go through with the Rings as defense against Sauron. But again, Sauron told her to go through with making them. She knew he wanted them to exist. Upping the amount from two to three doesn't change that (love how she thought that was some very clever loophole, lol; pls, she wanted to erase that they were originally intended to be wedding rings). So maybe her unconscious rationalization was basically: "My inner animus desires power, my externalized Animus offered to bind me to unlimited power, but I won't accept that--however, owning one of his brainchild Rings (that I will swear up and down are free of his influence!) seems like an acceptable compromise." x

"Once the projection has been withdrawn, then, the anima/animus can be recognized as a force within oneself" (TJC). I think this applied twofold to Galadriel's processing of Halbrand actually being Sauron. As mentioned above, because this is not a straightforward Anima/Animus integration arc, a few aspects happen the opposite way--so after her realization, instead of owning that she used Halbrand to pursue her own agenda, and that Sauron offered her exactly what she wants deep down, she spent from the revelation through most of s2 doubling down on, Actually, that was all him. She was given an excuse (and symbolically-psychologically, a decently logical one) to blame and deflect all her own desires and behaviors onto Sauron and his "deception", as if they were completely separate from herself. Both Elrond and Adar called her out on this and definitely struck a nerve. x x

The other potential application is more straightforward, if not complete. As others have pointed out, there's definitely something (multiple things, actually) within the fact she gave up a dagger--a phallic symbol--to make it into rings--a feminine/yonic symbol.* Through the lens of anima/animus, this can be read as, now that she'd finally found Sauron, and realized that she could no longer depend on Halbrand to carry the externalization of her ideal Animus, she was no longer animus-possessed. It's not reconciliation with her animus, but it's on the way there.