How about any of the Metroid games? Remember Samus is female.

If you've never played these, go for Super Metroid, it is by far the best. (SNES)

Then either Metroid Zero Mission (GBA) - remake of 1st ever Metroid, graphics based on Super Metroid.

Or

Metroid Fusion (GBA) - again, graphics based on Super Metroid.

In numerical sequence, Zero Mission is 1, Super Metroid is 3, Fusion is 4. (number 2 was on GB, kinda sucky)

I wouldn't go for anything like Prime though, the 3D format ruins it - like worms - always meant to be 2D.

Don't let Metroid's age put you off. Very clever games, definitely worth playing.

Oh, I almost forgot - you can of course emulate these on your PSP - with CFW of course. (did I even need to say that?! Meh.)