People have already made mention of Saints Row 2, and a few other games that allow you to do something similar if you so choose. At the end of the day your not going to see much in the way of "realistic" games with a female criminal lead where you actually go out and do stuff because it's extremely rare. Most criminal organizations and syndicates are extremely sexist, The Mob, The Yakuza, etc... and sometimes a point is made out of this in games and movies involving them. While there have been women achieving high ranks in such organizations it's largely been more of a political and social thing, rather than something they seized for themselves through the kinds of violence and action we're talking about and which would make for a fun game. Your typical "Mafia Princess" generally gets things done by being more of a Mari Hati type who nobody sees coming or takes seriously. Female "bangers" have existed, but as a general rule they tend to be very subservient to men, not in anything like top tier positions. In some respects having a female executioner in a Mexican crime cartel (which someone references) can be seen as an insult to the victim in an environment where Machismo is very much alive.
See, a big part of it is that men and women are not created equal, when it comes to violence and physical abilities men are way ahead. Unlike fantasy skill can only get you so far, and again such advantages rely on the assumption that the guys being fought don't have skills themselves. In reality "hard boys" take their fighting very seriously, work out constantly, and practice fighting. Your not generally going to see real world scenarios where some dude who knows kung-fu whips up on a bunch of thugs because none of the thugs actually know how to fight, today anyone who intentionally sets out to make a lifestyle out of fighting learns how to do it. Gyms and such can be big time hang outs for this kind of dude for that reason.
That isn't to say that a game like this couldn't be made, but it should be noted your going to be going firmly into fantasy territory to begin with, much like Saint's Row, which gets away with it by simply being so ridiculous and over the top with what the character can do that gender just doesn't matter anymore. Saint's Row also uses the unlikely premise of having a central gang which is somehow devoid of all of the racial, cultural, and historical elements that tend to hold such organizations together. When you've got whites, blacks, Hispanics, Asians, etc.. all working together on the street, even with the original premise of a "militant neighborhood watch organization" that started it all and the only ethnic gangs are bad guys who themselves downplay the race and cultural angles for the most part... your so far outside of real life crime drama and any pretensions of realism it doesn't matter anymore. Sort of like how you had Lucy Liu's character uniting the Tokyo underworld, which she did by being able to (easily) kill anyone who disputed her on ethnic or gender based grounds... it's a fun idea, but not even remotely realistic, as realism is not what the movie was going for, especially at that point... it was all about spectacle.
For the record "Breaking Bad" with a female protagonist already exists it's called "Weeds", and the central premise is very similar. A generally good person goes into the drug trade (in this case Weed instead of Meth) and it snowballs out of control leading to her becoming a "player" in the drug underworld and changing as a result. The style is very different however as fitting a female protagonist, half the point of the show being that this generally doesn't happen, and finding occasionally absurd ways to deal with the associated problems. Basically she doesn't go out and personally start brutalizing people or doing cool stuff that might make a good subject for a video game.
That said I'd be all for another game that went back to the old Saint's Row 2 status quo, being campy and ridiculous without reaching the later levels of absurdity, and still being focused on crime, as opposed to say fighting international syndicates made up of mad scientists and Luchadores, or fighting aliens in a VR sim. That came close and made the female protagonist work within context.
Perhaps more accurately a good idea might be to have the next sandbox "Super Hero" game involve a female lead, and more differences in terms of your morality choices. In something like "infamous" the inclusion of super powers explains why a woman could say subvert the underworld to her control if she went bad. The same could be said of "Prototype" if they used that basic power set and then didn't make the genetic terrors deriving from it being 100% the focus of the entire plot. I never much liked the idea of Prototype plot wise, but the powers in that game were a lot of fun to play with.
Now, some would find it sexist to say that you need to divorce from reality to have a strong, empowered, woman doing this stuff in this context, but that's largely because of how the world is. See, I'm sure out there have been some nasty female criminals, I mean heck Bonnie and Clyde are famous. The thing is though that they stick out as being exceptional because they were women, it's not normal. Tossing another one out there doesn't work because if this other character existed those other ones wouldn't have stood out, what's more if it was normal the current status quos within gangs and such wouldn't exist. Plus as I pointed out, there are usually exceptional circumstances. Sort of like using Annie Bonney as a justification for female pirates, when really she became famous because she was on the arm of a dude who was the actual captain doing the piracy stuff and holding everything together. No crew ever followed her. She's famous now for being a woman, but technically she's more an accessory to the legend of Calico Jack. When it comes to Bonnie and Clyde, Clyde was the guy who did most of the infamous stuff, like winning a shootout with the police when cornered in a motel because they all had pistols and he had a BAR (Browning Automatic Rifle) which was an unprecedented amount of firepower for the day and caught them entirely by surprise.