I'd think the key ingredients are looping, stabilization, roto or keying, masking, distortion, the puppet tool -- and storyboarding. Lots of storyboarding.
You also need the right kind of source material. Notice that the body of the sheep doesn't actually move all that much.
Stabilize the footage so that it's as static as possible, then loop it. Isolate the parts you need, animate to taste, and add some natural-looking motion that you stabilized away back in.
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