I've never cared about backgrounds in character portraits so I'm only reviewing the art style character herself; I like your mixed chibi style, it's pretty good. The shading is simple but pretty effective. Now, as far as strictly her design- She seems too smiley and cute to be wielding a revolver. Don't take that as a harsh thing, I just think a pair of slanted, devious eyes and a more sinister smirk would work better for her. If you draw her in non-sprite form again, I'd suggest putting the creases of her hips more at an angle and longer, not trying to be gross, but it looks like she's rocking a cameltoe.
Furthermore, if you're interested in making a game, Stencyl and Construct 2 are two programs I know of that require little to no programming and involve a GUI interface to create instances to put together games, it's great for platformers as far as I can tell, however, I unfortunately lack the motivation right now to learn even the simple functions require to put together a game.
If you do, more power to you.