And yes, I do mean 3! Obviously, I didn't get this as a speedrun, but I got through it as fast as I could. Even with slow-downs and savestates, I was jerking back-and-forth between moving RoboCop and saving/reloading a state. Does it help to use that FCE movie editor by any chance?
Game starts at Power-on/Hard Reset and it ends when RoboCop enters the very last digit at the top of the OCP tower. My first attempt was 6:30 - call mine a no-death run if that counts. =P Again, I am sure someone out there can do it better.
http://dehacked.2y.net/microstorage.php/info/1828280988/RoboCop3_F.fcm
A few things to look at when you do want to play this game again and do make a good speedrun out of it. All of RoboCop's jumps in this game are NOT pressure-sensitive. When picking up a missile upgrade from regular to homing, you'll only get 5 of these. Plus, there is a good chance where Robocop will go to repair laboratory with no efficiency upgrades, therefore, it is best not to waste frames by hanging around there.
You'll get some relief after defeating some strange metal-gear-wannabe walking tank and proceeding to the top of the OCP tower. Example, say you had 76% efficiency and you defeated the walking tank with only 52% or something like that. You might start the OCP tower stage with the same efficiency you had before (76%). It is important to carry plenty of efficiency to the top of the OCP tower! This way, you might be alive long enough to input a 16 digit code that will kill both ninjas and end the game. I would recommend at least 85%. You might get by if you stand at the computer and jump as soon as either or both ninjas swing their machetes, but that takes timing.