Here is the full list of all 41 Chessaria: The Tactical Adventure achievements.
Save Horsan
Save Queen Aria Kasparian
Encounter a dragon
Save Turim
Save Bishop
Defeat your first creature
Save King Magnael Kasparian
Defeat Goliath, the Golem
Defeat Astralion
Stop the horde
Defeat Volgan, the Orc King
Defeat Leefa
Defeat Volcane, the Dragon
Encounter a Nymph
Save the Elven Guards
Save Leefa, the Fairy Queen
Unlock 2 boards for Quick Game
Win against the computer in a row: x2
Win against the computer in a row: x5
Win against the computer in a row: x10
Win against the computer in a row: x15
Win against the computer in a row: x25
Play against the computer: x1
Play against the computer: x5
Play against the computer: x10
Play against the computer: x20
Play against the computer: x50
Win against the computer: x1
Win against the computer: x5
Win against the computer: x10
Win against the computer: x15
Win against the computer: x25
Play against a friend: x1
Play against a friend: x5
Play against a friend: x10
Play against a friend: x15
Play against a friend: x20