Here is the full list of all 9 Chess: The Lost Pieces achievements.
Complete 10 puzzles
Complete 20 puzzles
Complete all puzzles
Join the Chess: The Lost Pieces discord server!
Beat the story mode 1 time. Unlocks "Reversant"
Beat the story mode 3 times. Unlocks "Cavalry"
Beat the story mode 2 times. Unlocks "4D Knight"
Beat the story mode 4 times. Unlocks "Vampire"
Beat the story mode 5 times. Unlocks "Rifle King"