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