First I try to kill them when they cannot see me. That could be shooting around corners, or blowing up acid barrels etc.
Next if I have to face them in sight, start running and use a shotgun. The running mode makes a lot more of the enemy shots miss, but doesn't affect the accuracy of the shotgun. Note be aware of what is behind you, in case his shot misses you can still be hurt if standing next to a wall or acid barrel etc.
I feel reasonably competent in this game now and can handle most enemies up to Hurt Me Plenty. I even won the game on Ultra-Violence once with some luck. But Nightmare difficulty just seems impossible. I would love to see a replay of someone playing Nightmare successfully.
Tips for Nightmare, anyone?