* Mug the red duck-creature in the first episode
* Red triangle on cliff wall - must slide-scurry to far R of map for coin
* Far R of map, creates coin at red triangle on cliff wall
* Several on the Sand Bird level
* Sand bird lvl - Go up to top of hill and shoot down blue bird for blue coin.

* Lvl 6 - blue coin in water to left.
* Lvl 6 - another in water to right. You have to chase it.
* Lvl 6 - There's a third in the water.
* Lvl 6 - A fourth is from the swing - just get onto the swing and use your jets to get you swinging!

In Gelato Beach, There's a hidden blue coin in episode 2 or later. Go to the place the sand castle popped up in episode 1,and spray to get a shine sprite-like shape. Get it! ;-)
-- from Al

Super Mario Sunshine Walkthrough