The Great Beast is a deceased creature whose bones lie in the ruined temple of Shark Tooth Island.
Role On Shark Tooth Island
While exploring the Temple of the island, Fruit Bat Man will tell you that he senses the bones of "great beast". You need one of the Great Beast's bones for the Calming Potion. You can take the one lodged in its jawbone. The skeleton lies at the bottom left of the temple, when you fall down after getting past the moving platform.
It is unknown what species the Great Beast is of, but it was probably a predator based on its sharp pointed teeth. It is most likely a shark or a dinosaur, however, it is possible that it could be some sort of reptile based on the shape and size.