So to start off, here is the first hidden animal from the outback. Bunyip is the first one. If you want to unlock Bunyip, pass 2,000 meters and then you will see Bunyip on the edge of a cliff. Once you do, jump on Bunyip and then catch it and you will have it available to unlock.
Bombat: If you want to get Bombat, then ride on a wombat. Get the wombat angry, and then smash into three animals. When that happens, Bombat will appear: smash into it and you will be able to catch it.
Cameleon (Camel): To get the Cameleon, which is a color changing camel, first start off with an animal that doesn’t start on that island. Then ride 8 different animals in a row and the Cameleon will appear.
JURASSIC: Stegosawrus: To get this one, hop on a regular stegosaurus and then eat nine shrubs in a row. Once you do that, the Stegosawrus will appear. Ride it and you will be able to catch it.
TUNDRA: Fairy Penguin: For this one, start off with an animal from a region other than tundra. Then once you do, ride on nine different animals in a row. When you do that you will be able to unlock the Fairy Penguin.
Beyond that, there are some unresolved tips out there that can possibly lead to other secret animals. One of them says that you must ride rabbits in a row. The other one suggests that you must ride a number of different animals in the tundra. Do one of these things and you could figure out the animal that nobody has figured out yet.