Water Eggman (ウォーターエッグマン) is the second boss of Sonic the Hedgehog 2, appearing at the end of Chemical Plant Zone.
This is a tricky boss in that the floor panels on each side of the player flip over, kind of like trap doors. That being said, the player has to be careful as to not be on any one of those platforms while they turn over, or else they'll plummet to their death. The trick here is to simply bounce on Dr. Eggman 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 the player, though this can be avoided by jumping over the chemicals, whic is not hard at all to do so. Alternatively, if playing as Sonic, the player can duck when Eggman drops the chemicals; it won't harm them. After eight hits, the boss is defeated.
It is possible to defeat Eggman in one go if the player stays on top of him when he enters the arena. Unfortunately, due to timing issues, this will lead the player to fall to the platform while the surface is underneath, causing death. The remedy for this is to count to seven hits, then pull left to land on the middle (static) platform and dodge the chemical drop to hit him once on the left hand side. In the 2013 remake, this is the easiest way to get the "Bop Non-stop" achievement.
In the final build and all prototype builds of Sonic 2, sprites have been found of Eggman 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.