Purple is a good start I think, or just blue even though that is Ruby’s flipped color as well. I think Purple could be a nice unique color to her, at least for her hair.

I looked up what the “opposites” for bronze would be, and this Steel blue popped up, ask well as this sort of purple for the opposite of a brownish color. Then maybe have silver or regular gray steel for her armor, circlet, and necklace instead of gold? And should we change her eye color as well like with Bleiss having red eyes instead of lilac?

Okay so here's what I am thinking are some strong points:

She has hair like the red-violet color hair like in the first pic

Her bronze and brown corset is now steel blue and the purple in the third pic

Her golden accessories (circlet, necklace, and armor) are now silver instead

Blue eye shadow perhaps?

As for flipped Pyrrha’s actual personality itself, I do have some ideas as well:

She is much more arrogant and acts more entitled than regular Pyrrha, fame from being the "Invincible Girl" having long since gotten to her head.

She believes that she is actually better than a lot of people and loves the attention she gets from her fame. This can make her kind of difficult to work with

She show less restraint when fighting and barely any sportsmanship when she thrashes her opponents, gloating in her victory

She's also much more bold and free spoken with people, not too concerned with what people think of doing so because she's the Invincible Girl so therefore her opinion matters most. She'll outright tell someone that they're annoying her or that their ideas are stupid

She's a huntress more to keep proving herself as the strongest rather than to actually help people

Now for her name. On the RWBY wiki it says that "Pyrrha Nikos's "first and last name together are a reference to a Pyrrhic victory, a tactical victory that comes at such extreme cost it is often seen as a strategic defeat" and that ""Pyrrha" is derived from the Greek adjective pyrrhos (πυρρός), which means "flame-colored". Nikos (Νίκος), meaning "victor of the people", is derived from Nike, the Greek Goddess of Victory." So perhaps something else since her hair color is different that "Flame-colored" now and is purple instead as well as a different last name as well to fit her more arrogant nature?

Now, "According to the Merriam-Webster Dictionary, the word “purple” is derived from the Greek porphyra or porphyrous, a seldom used adjective describing “someone that has a purple color.”" and her last name could have to do with hubris, derived from the greek word hybris who was a spirit (daemon) of insolence, violence, and outrageous behavior. Also hubris basically means arrogance, which would fit this flipped version of pyrrha nicely

Here are three name ideas for her that I have from most favorite to least favorite:

Phyra Hybos

Porphyra Hybros

Porpyra Hybos

Super subtle, I know. Or maybe a different combination or alteration of these, but Phyra Hybos is honestly my favorite because it's similar enough and different enough to Pyrrha Nikos in my opinion. So that will be the name I work with for now unless enough people like something else.