So do you have a problem with males being edgy and badass too or is that something you feel that only men are allowed to be?
By saying "edgy and <<badass>>", I thought about an edgy psychopath like Catalina or Trevor. I think both women and men can be like that though.
What exactly do you want out of a female protagonist?
Here's an example copy-pasted from one of my older posts:
How a about a female protagonist who is into illegal street racing, stealing cars and the likes? This idea doesn't require RPG-7's and other heavy weapons (so people who think that women can't use rocket launchers or miniguns won't take the idea "too unbelievable"), it's still related to crime and isn't sexist (I mean, it doesn't force a protagonist to do some whore's jobs).
inb4 "women can't drive a car" or "women only drive small-ass compacts"
E: 10th page! Wow.