Carnival Island

Carnival Island features a total of 36 pets that will cheer you on during the games. 35 of them will be unlocked by completing one challenge for each of the 35 games (it doesn't matter which challenge you complete). Below I've listed those 35 pets and in which game you'll get them (NOTE: the list is based on choosing the Panda as your starting pet. If you choose another pet as your starter you'll get the panda instead of your other pet):

Mini-bowl:
Mini-bowl - Mammoth
Snake in the Grass - Rabbit
Jackpot Lane - Swallow
Knock 'Em Out - Cat
Rollin' Racers - Civet

Ringers:
Ringers - Mouse
Rockets - Fox
Narwhal Rings - Dog
Peg-It - Owl

Hoops:
Hoops - Aardvark
Topsy-Turvey - Elephant
Hot Shot - Platypus
On the Move - Tapir
Triple Threat - Duck

Frog bog:
Frog Bog - Hippo
Hopper Boppers - Jellyfish
Flyin' Frogs - Goldfish
Water Wheel - Walrus
Swamp Gas - Lake Monster

Coin Toss:
Coin Toss - Sheep
Nom Nom - Boarder Collie
Gold Digger - Kiwi
Teacup Towers - Meerkat
Roundabout - Triceratops

Shooting Gallery:
Shooting Gallery - Narwhal
Bandits - Raccoon
Raccoon Saloon - Turtle
Fort McCannon - Chameleon
Shoot Out - Numbat

Perfect Pitch:
Perfect Pitch - Prairie Dog
Wrecking Ball - Kangaroo
Gopher Trouble - Koala
Flip Four - Dodo Bird
Boom Town - Sugar Glider

To obtain the 36th, pet you'll have to buy the Confetti Cannon - see the Cannon-Aid trophy. After buying it choose it from the Boardwalk map. Then just keep firing the cannon until a pet comes out of it.