Piper is the titular protagonist of the 2016 Disney/Pixar animated short of the same name. She is a sandpiper hatchling that suffers from aquaphobia (fear of water). Despite this, she is taught how to overcome her fears with the help of a hermit crab.
Obviously, don't nominate any human characters. Hybrids like Cheetah or The Lizard are okay, as are shapeshifters with one set animal form (eg Professor McGonagall.)