Where are the secret shine sprites in super Mario sunshine?

They are in every level that your FLUDD is taken away (except the goopy inferno in Pianta Village). Once you defeat the level, you reenter the same level and find the red switch. It looks like a lump and is the first thing you will see. Ground pound the switch and get all eight red coins in the level within the time limit. Once you get all eight, a Shine Sprite will appear.

You can also collect blue coins. They are hard to find, but collect ten and you can trade them for a shine sprite in the boathouse.