Let's play: Iji
Official site
TIG source database entry
Iji is an action-packed platform shooter that features a detailed story, large levels with multiple paths, powerful bosses, and lots of secrets. There are alternate gameplay events, dialogues, and scenes that change depending on your actions. Iji, the protagonist, has superhuman strength and abilities which she can upgrade. She can fight with Nanotechnology, crack systems, and even use her enemies' most devastating weapons against them.
I've been playing this game for the past few days, and i love it.
Very story driven, but lots of action and it gets pretty hard on the higher difficulty settings too.
I really like how you have stats, you start out at level one, and you gain 3-5 levels per sector you complete (amount depends on the difficulty you are on).
There are a good amount of extras in it, 8 weapons, each weapon can be fused with another so you can have a total of 16 to play with
Best of all, its free, so go try it!