Here is the full list of all 14 Animated Puzzles Star (Windows) achievements worth 1,000 gamerscore.
Complete the cow puzzle in stripes. Begin with top left corner. (Normal difficulty)
Complete all tiers
Get a medal in Daily challenges
Complete a tier puzzle in all difficulties
Complete tier 1
Complete all tier puzzles with hard difficulty
Complete all tier puzzles in all difficulties
Complete all tier puzzles with three different shapes of puzzle pieces
Complete the "sunset house" puzzle upside down (Normal difficulty)
Begin a battle
Win a battle
Get a diamond medal in Daily challenges
Complete the dandelion puzzle like a checker board. Begins with top left corner. (Normal difficulty)
Complete the "black cat" puzzle within 2 minutes. (Normal difficulty)