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