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