Hydrocity is the second zone of Sonic 3, and as indicated by the name, there's a heavy emphasis on water here. Whether you find yourself on a boat or in a bubble underwater, the traversal of this stage is certainly unique. The achievement/trophy for this zone requires you to find three boats in the first act.
Act 1[edit]
After being whisked through in an underwater tunnel, you should end up hanging on a hook. Before this hook can send you in another direction, hop to the next hook to the right. This will shoot you upward. Continue to the left until you come across a gap you can jump over. Across the gap are some fans that you can use to reach a platform and some conveyor belts. Cross these obstacles and continue to the right. The momentum should lead you to a tunnel high up in the wall. Enter for a Super Ring Item Box, and drop down past a crumbling platform to land on the first boat. When the boat reaches a wall, you'll have to grab a hook to lower the water level, then drop back down to the boat to continue floating along the water. Duck to avoid some spears, then continue to the right when you reach land. When you come upon some bubbles and fans, use a Spin Dash to reach a hook that raises the water level. Jump into a bubble and maneuver it along the fans, toward a spring to the right. You should break through to another level, at which point you can drop down to the right to ride the second boat.
Once you come upon land, continue to the right. You should eventually find yourself on ground underwater. Climb some blocks to the left to reach a hook that lowers the water level, then continue to the right, not doing anything to alter your course until you come to a stop. Hop on the spring underwater to reach a fan, which will allow you to reach some floating blocks to the left. Climb up through a gap in the ceiling using a bubble maker on a platform to the left (if playing Tails, you can simply swim up here) and some fans will appear under you, lifting you further up. Once out of the water, continue to the right to find the third boat. The path to the final boss is pretty straightforward from here, though you'll have to escape the shifting ruins first.
To defeat Dr. Eggman, you'll have to take control of the Egg Mobile. Use the jump button to spin the propellers when Eggman is directly underneath them; this will suck the water up from the pool that Eggman is swimming in, and Eggman with it. As he comes into contact with the propellers, he'll take damage and fall back into the water, requiring you to find a prime opportunity for another hit. Be careful to avoid bringing any of his bombs with him, as these will only do damage to you. As long as Eggman is isolated, you'll be able to bring him up into the propellers and get a hit in on him. Try to predict the direction he'll be swimming in and begin to bring the water up early, as there's a high chance he'll swim right into it; even if he is followed by some bombs, as long as he gets hit first, you can drop the current before the bombs can reach you.
After four hits, Eggman will give up and fall into the depths of the water, allowing you to hop out of the Egg Mobile and run into the Signpost.
Act 2[edit]
The second act is mostly straightforward. When you first end up underwater, you can enter a tunnel to the left to find a Water Shield, which will let you breathe underwater without the need to look for air bubbles. At one point, back above water, you'll have to Spin Dash up a curve in the wall to reach a lift. This section should be familiar to you if you've played this zone in Sonic 3. Otherwise, this act should move much quicker than the last, leading up to another encounter with Eggman. This time, you'll be moving swiftly through the water (if you still have a Water Shield, you won't have to worry about looking for air bubbles). Touch the bombs to set them off and Eggman will collide with them, damaging his latest machine. Do this four times to get him to give up and face the second phase of this boss.
In this second phase, hit Eggman when the rockets that orbit him are out of the way, and use a Spin Dash to dodge him when he charges underwater. Occasionally, he'll have the cylinder in the middle of the water spin in order to cause you to float around it uncontrollably; this slows down your progress, but doesn't actually do anything to hurt you. After your eighth hit, Eggman's machine will fall apart and the water level will lower. Free the animals to proceed to the next zone.