Tip from Dan

There is an entrance to a Red Coin Collection Game on the island across from the beach with the two umbrellas. This island contains a palm tree, a stranded man, a small fire you can put out for a 1-up mushroom, and a green manhole covered with rippling yellow goo.

The entrance to the Red Coin Game is through this green manhole, once the yellow goo has been washed off. The only way to wash this goo is with Yoshi's juice.

Half of the difficulty of this Red Coin Game, is getting Yoshi out to this island, given the fact that he cannot go in the water. Obtain Yoshi, then hop on the boat to get to the other island near the entrance to the canal. You can also get out there through a tunnel. Once on that island you must wait for the second boat to come that makes a loop between the island and the platform in the middle of the ocean. Before hopping on this boat when it arrives, be sure to refill Yoshi's juice with the fruit in the tree. Once on the second boat, ride it to the platform, jump on that platform to wait for the third boat. Eat the bannana to refill Yoshi's juice once again. The third boat will bring you to the island containing the entrance to the Red Coin Game. Spray the yellow goo with Yoshi's juice and you are IN!

Collect all 8 Red Coins in the secret canal while riding the lillypad. You will die if you fall in the water. Use Mario's Water Gun to attempt to direct the lillypad.

I assume if you get all 8 Red Coins, you will get a Shine, but I haven't been able to do it yet. Believe me, its difficult. The lillypad sinks after a period of time and really won't move against the current.

Super Mario Sunshine Walkthrough