The crab is an animal that appears in the island underpass and the beach off of jungle town. It can be purchased and has a quest that can be completed for an egg.
The crab can be found in egg form by heading to the sapphire cave, which can be accessed with any level 3 pet.
Once inside, you will be met with pillars of rock infront of a waterfall.
You must collect 30 Sapphire, and parkour up the pillars to meet the Crab Leader, who will give you the crab egg in exchange for the 30 Sapphire.