The Animal Spirits appeared in the episode Blind Trust where they were discovered in an ancient animal burial ground.
After Pops takes the three of them up to the top of a mountain to test Benson on his trust for Mordecai and Rigby, Mordecai jokes about how Benson was blinded by nature. Benson then walks off and tells the two of them he is going to find his way down the mountain himself, despite being unable to see. Mordecai and Rigby still follow him, though, warning him about rocks in the way.
They eventually find their way to a path, and Benson feels a sign that warns about an ancient animal burial ground. He thinks that they've found the main path, so despite Mordecai and Rigby's warnings, Benson walks towards the burial ground, knocking over piles of rocks which release the Animal Ghosts, including a moose which warns them to turn back.
The spirits all share a pale green color for their fur/feathers, in addition to dark green eyes which is the common ghost colors in Regular Show.