Who reduces Animalism to the phrase "Four legs good, two legs bad"? Also, who teaches the sheep to chant "Four legs good, two legs better"?

The answer to this question can be found very close to the beginning of Chapter 3.  The answer is that it is Snowball who comes up with this way of boiling down the commandments.  He says that if any animal could just remember this idea, they would be safe from being bad like the humans.

This sort of goes along with the idea in the beginning of this chapter that most of the animals were just too dumb to learn much.  Because they were too dumb, Snowball needed to make the commandments simpler so that everyone could understand them.