The game I'm thinking of is about a guy, his city is over run with these alien mutant things, it's quite bloody and gory. It's a side scroller shooter as well. You could use multiple guns, grenades, when the enemies would die they exploded in like a green or red gore.
First hint: A story-driven platform game that doesn't have any kind of (understandable) dialogue. In fact, the only words you can read are the name of the game, a few non-important ones in the intro and THE END when you beat the game. :p