Three words: HIT AND RUN. This tactic has kept me alive a lot longer than just staying and shooting madly would have, considering that once you're hit, you can't hit anyone else for a short period of time, and as soon as you're not invincible anymore, you can be hit again, putting you in a state where you can't hit anyone.

Adjoining to the previous tactic: DO NOT CHASE. At any second during when you are chasing your opponent, he might just turn around and blast you right in the face, or jump over you and shot you from behind. Actually, come to think of it, these might be good ideas of you are the one being chased.

Another good tactic is DODGE EVERYTHING. Keep moving in an erratic pattern and, soon enough, your enemy will lose track of where you are. (This is where the Caps Lock button comes in handy.) Then find your way to being behind him, and blast to your heart's content.

Lastly, make sure you know a little quirk in the level that the other person doesn't, such as that seeker powerup warp. It might lead to, indeed, a powerup, and powerups are always good. Unless your opponent has them.

Hotel levels are evil.