Proposed Game: Arkham Knight
Wealthy? Trained in combat? Tragic backstory? No, I'm not talking about Batman. I'm talking about Kate Kane. Unlike Bruce, Kate built her foundation in combat while attending a military academy. After her commanding officer discovers she is a lesbian in a relationship with another student, she is forced to leave the school and returns to Gotham, where she eventually takes up the mantle of Batwoman.
Kane is heard on Bruce's answering machine in Arkham Knight, talking about her engagement to Maggie Sawyer and alluding to her secret identity. It would have been extremely cool if she appeared in-game as one of Batman's allies and a playable characters in the game's "Dual Play" feature, allowing you to switch between characters seamlessly during combat.