It seems to me that woman protagonists tend to be ones who complement an "indirect" approach to problems.
For example, Catwoman in Batman: Arkham City couldn't glide like Batman, or even pull herself directly to gargoyles, instead she always had to pounce and climb and so forth, taking much more complex routes around the environment, her moves for dodging and fighting were much more elaborate, presumably for psychological effect, her enhanced vision mode was a representation of various senses such as air currents, heat, smell, and passive echolocation, things she doesn't so much "see" as experience in ways alien to the player.
And then there's Chell from the Portal games, It's a game all about thinking outside the box, GLADOS, who's sort of female, challenges you to do so within the chambers, but the chambers themselves prove to be a box for the even more female Chell to think outside of.
Tomb Raider, where Lara has to work out ways to beat the ancient engineers, not by breaking or overpowering their systems with modern technology, but by testing, predicting, and outpacing them, thinking and moving in ways the ancient engineers presumably weren't aware of. Even the gunplay is focused on keeping your distance by running and flipping around rather than aiming or using cover.
Mirrors edge has Faith beating plenty of armed enemies, but if you're doing the pacifist run, (how I say it's supposed to be played) you either defeat them by doing the opposite to them, running away, or you find ways of approaching them without being in their view long enough to get shot.
