I know I’m probably going too in depth into this, but if you wanted to make an accurate Batman DnD character I suggest a artificer/rogue/monk multiclass with subclasses in artillerist, assassin, and way of mercy respectively.
I say artillerist because of all his throwable, exploding batarangs, smoke bombs, air capsules, etc. also being an artificer allows him to create all his fun toys that would be considered magical in dnd. Rogue is for obvious reasons but I chose assassin specifically for its disguise elements, Batman is a master of deception and at a decent level an assassin rogue can perfectly copy how someone looks which is something Batman does often (Matches Malone). Lastly I chose way of mercy because Batman is a pseudo medic for his team, also it allows the flavor of different fighting styles with the hands of harm ability you get with choosing the subclass.
Race would be human obviously, but if your dm allows it I’d choose variant human with either the observant or crusher feats but personally I’d choose observant to move more into that detective style of Batman. But if you choose the aforementioned monk multiclass crusher would be the way to go, those bludgeon damage bonuses would go very well with hands of harm.
Obviously background would be noble, do with that as you please.
With standard array stats I’d go as follows; Strength (10), Dexterity (14), Constitution (15), Intelligence (13), Wisdom (8), Charisma (12). My line of thinking is that Batman is an overall very high stat character, and you can buff the lower stats later with racial, class, subclass and leveling bonuses.
Anyway this has been your in depth Batman DnD guide, hope you enjoyed.