Sea Slide Galaxy is accessible in the Engine Room with 36 Stars.
Star 1: Going after Guppy
Swim up to Guppy and talk to him. Follow him and go through eight rings that he makes. Collect a shell on the way to make it easier. Once you have gone through all the rings, collect the Star he releases.
Star 2: Faster Than a Speeding Penguin
At the underwater cavern with the giant eels, you have the option of taking the left-side or right-side path. Take the cavern on the right. Despite the fact that the left one has an accelerator circle, it is much easier to win by swimming through the shorter tunnel on the right. Note that if you pre-swim the course, you can kill the eel in the left cavern tunnel (with a shell) for a 1-up mushroom. The right-side eel will give you star bits if killed.
Star 3: The Silver Stars of Sea Slide
For the time being, ignore the Hungry Luma you meet on this level.
Star 4 (Cosmic Comet): Underwater Cosmic Mario Race
Grab a red shell. Use three rings to boost your speed. Jump out of the water and find the Star behind a building. You might want to throw away the shell (by spinning) to allow a long jump once on dry land.
Star 5 (Purple Comet): Purple Coins by the Seaside
100 coins, no time limit. All up high (Bee Mario - use short bursts rather than continuously holding down A to get from cloud to cloud) or on ground - none in water.
Star 6 (Hidden): Hurry, He's Hungry
Enter Star 3. Proceed through the level as for Star 3. When you reach the the hungry luma, feed it star bits and it will turn into a cannon. Use it to shoot to the galaxy with the green platforms. Collect all the notes and the star will appear.