This is probably the most important thing, always keep moving, never stop. Don't linger in the same room for a long time, don't try to 'camp'. Plenty of weapons in this game heavily punish a stationary target/style.

Even in a 1v1 fight, its important to move: Strafe left and right against Machine gun/Shotgun/Lightning gun/Railgun. Delay your strafes a bit against Nailgun. Keep jumping against Rockets/Tri-bolt.

Try to not chase your opponents. Easiest way to get ambushed, die a horrible way. If your target escaped, go find health and armor, and look for the next opportunity to murder them.