Bee Eater, Blue Jay, Chaffinch, Chickadee, Crane, Jackdaw, Kingfisher, Magpie, Nightingale, Oriole, Roadrunner, Singing Bush Lark, Waxwing, Woody, Wren and Yellow Wagtail

Easy
fox, hedgehog, mole, brown bunny, grey squirrel, wren, wagtail, chaffy, cuckoo, raccoon, hare, singing bush lark, skunk, gecko, camel, donkey, deer and magpie

Intermediate
Tortoise, Lop bunny, meerkat, road runner, armadillo, piglet, ostrich, chipmunk, coyote, wolf, bee eater, guinea pig, giraffe, woodpecker, barn owl, zebra, crane, toad, blue jay, seal, king penguin, puffin, walrus, platypus, otter, sea lion, Llama, chickadee, prairie dog, Aardvark, gazelle, leopard, oriole, bandicoot, sugar glider, Hippo, roo and wallaby

Advanced
red squirrel, waxwing, kiwi, porcupine, fairy pink armadillo, badger, Olinguito, nightingale, elephant, Long eared owl, Australian king parrot, pair of magpies, jackdaw, king fisher, ferret, rockoon, froog, snabbit and ping-pong, giant ant eater, tiger, wombat,  koala, taz, giant panda, red panda and gorilla

Jumps I know of so far and important to remember.
Toad to tortoise
Gorilla to kingfisher
Jackdaw to Red Squirrel
Bee Eater to Aardvark
Prairie Dog to Gazelle
Magpie to raccoon
Wallaby to blue jay
Cuckoo to Fox
Aardvark to Guinea pig (thanks Susan)

As we have all started the quest's at different points for the wildlife critter's, some will have jumps, the above are the jumps I know of their maybe some more, and I will add them as and when I find them, anyone knowing of more please let me know.
UPDATED

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2940 white uni
5699 roo
2970 ostrich
2952 leo
2954 woody
2986 black uni

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1Kangaroo
2Giraffe
3Crane
4Skunk
5Unicorn
6Elephant
7Winged Unicorn
8Tortoise
9Black Unicorn
10Grey Squirrel
11White Unicorn
12Leopard
13Baby Unicorn
14Hedgehog
15Golden Unicorn
16Woodpecker
17Badger
18Zebra
19Meerkat
20Ostrich
21Rainbow Unicorn