The beach is all goopy! You only have 3 minutes to clean it up. You really have to do a good job of getting all the goop out, while you might be able to leave a spot or two, they want the vast majority of it cleaned up.

Note that there are 2 kids and 2 parents in the center area - make sure you clean them thoroughly! Use run and blast-sweep method and you can get most of it clean. It chimes when it's done, around 12 seconds left usually.

Go back and talk to him. He'll give you the shine.

Super Mario Sunshine Walkthrough