I was bored today. Extremely bored. In fact, I was so bored, I did the first two levels of this game, plus the bonus "training" level. Here you go. "Enjoy" the movie.
http://dehacked.2y.net/microstorage.php/info/601237332/Robocop%20%28U%29_bleh.fcm
Yes, the best way to avoid things is to use the "block" move (stand still and press select), which makes you invulnerable for about a second or so. You can't do it on stairs, though, which is why I have to take a hit at one place (killing the guy would take longer). I'm also not completely happy with the second level boss fight, but it looks pretty good at full speed, so I can't be bothered to improve it (if it's even possible). Also, it's probably possible to manipulate the enemy spawning so you don't have to use the block move so much (it slows you down by about 3 frames each time you use it). Now if you'll all excuse me, I'm going to shoot myself.
(I was unable to download the movie posted by braceyj since the link is about three years old and broken)