Sonic Advance/Zone 4

Act 1
Head to the right, until you reach the first tunnel.

After this point, you will need to go through an underwater section. There are three entrances, and to minimize the time spent underwater, you will want to try to go as far right as possible. However, if you enter a little early, you can look for air bubbles down and left of the four rotating platforms.

You should eventually come across a pillar blocking further access to the right, which requires a rather high jump. If you can't swim over it (like Tails can), head down, and use the bumper to throw you above that pillar. Reach the checkpoint, and get the air bubble on the platform to the right. Jump up, and use the spring to exit the water.

You will eventually need to return to the water. When you get there, jump in on the right-hand side of the spinning platform, and use the springs to jump across the bottomless gap (and another spring to exit the zone.)

Act 2
Like the previous act, there is water in this level. However, you can proceed through most of the level without even touching it, as long as you remain as high as possible.

Act 2 Boss
This boss fight takes place underwater.

Dr. Robotnik will walk across the cavern ceiling, and smash to cause icicles to fall. To damage the boss (in addition to getting air), you need to jump on the icicles, then jump at Dr. Robotnik to damage him.

As Tails, you can swim to the surface to get free air. Amy Rose doesn't need to use the icicle platforms, and can attack directly.