Here is the full list of all 14 Animal Herding achievements.
Pick up 2000 chickens
Complete the story
Get all stars in story mode
Get at least one star in all challenges
Complete all the challenges and get three stars in all of them
Get one star in all story levels and challenge levels
Get all stars in both story and challenge mode
Complete a level without touching a single animal
Defeat all bosses in challenge mode!
Pick up 1000 chicks
Return 500 foxes to the bushes
Stop 500 hedgehogs in their tracks
Grab 500 moles when they show themselves
Pick up 1000 cats