Water Eggman (ウォーターエッグマン), the boss for Chemical Plant Zone, is a tricky boss in that the floor panels on each side of you flip over, kind of like trap doors. That being said, be careful as to not be on any one of those platforms while they turn over, or else you'll plummet to your death. The trick here is to simply bounce on Robotnik TWICE in a row while he's docked on the side of the screen, filling up his giant vat with blue chemicals. When that's full, he'll try to dump it on you. Not to worry, just jump over the chemicals, it's not hard at all to do so. Alternatively, if you're playing as Sonic, you can duck when Robotnik drops the chemicals on you; it won't harm you.
After eight hits, the boss is defeated.
It is possible to defeat Robotnik in one go if you stay on top of him when he enters the arena. Unfortunately, due to timing issues, this will lead you to fall to the platform while the surface is underneath, causing you to plunge to your death. The remedy for this is to count hits to 7 in your head then pull left to land on the middle (static) platform and dodge the chemical drop to hit him once on the left hand side.
Note: In the beta, sprites have been found of Robotnik accidentally dumping the chemicals in his machine on himself. This may be a missing boss ending sequence similar to the one in Emerald Hill Zone.