Here is the full list of all 17 Curse of the Corsair achievements.
Complete the Tutorial
Complete the Ancient Temple
Complete the Pirate Stronghold
Defeat the Starfish
Defeat the Final Demon
Kill 100 Lunging Enemies
Kill 100 Thrusting Enemies
Kill 100 Ranged Enemies
Kill 100 Enemies
Kill 500 Enemies
Kill 1000 Enemies
Dash 5000 Times
Kill 6 Enemies with Just Melee Attacks
Kill 6 Enemies without Taking Damage
Acquire All Keys in the Game
Beat the Game without buying anything in the Shop
Defeat the Viking