Here is the full list of all 19 Curse of the Crescent Isle DX achievements. It takes around 3-4 hours to unlock all of the achievements on Windows.
Complete Speed Run Mode
Let a Carfee fall in the water
Hit the third boss three times on its way up
Find one of the special messages in the password screen
Complete a stage in co-op
Complete the Boss Rush Mode
Complete the game with no coins
Complete the game as the Queen
Collect all 27 coins in the game
Complete the game as the King
Defeat Aranomanom
Break one of those big rocks
Take damage by staying underwater too long
Talk to the statue in the town
Defeat Naja Naja
Defeat Grondor of the Forgotten Mine
Jump off an enemy while grabbing him
Complete a stage without taking damage
"Accidentally" kill an enemy