NOTE: This walkthrough only entails how to defeat the "real" Robot Master, and get the Beat Letter.
Centaur Man's stage is interesting because the laws of physics have, apparently, taken a vacation.
This is a pretty easy stage, though, and most of the robots here are very easy to kill. The mine enemies you encounter, will explode after a few seconds in the water, and when they do so, some harmful chunks of shrapnel will be launched, so exercise caution.
At the end of the stage, you'll see the Boss Door across a large chasm. Simply fly over there with the Rush Jet.
Centaur Man is this game's "time freeze" robot. Battle him with the Knight Chain, hitting him whenever you can. His two attacks are freezing time, and firing conventional arm cannon shots, which split into many shots when they hit the opposite walls. Just stay on your toes and thrash him with your mace ball, and he'll be pretty easy to deal with.