Here is the full list of all 38 A Hole New World achievements.
Complete Challenge Mode
Unlock all achievements
Complete the game finding all secret characters, secret items and gems
Find the secret banana
Complete Story Mode +
Defeat Lord Baduk in Stage 1
Complete the game in under 35 minutes
Complete the game killing no enemies at all
Defeat Lord Baduk and sustain no damage
Complete Boss Rush Mode
Defeat Super Baduk and sustain no damage
Complete Story Mode
Complete Story Mode with no continues
Complete the game and kill all the enemies
Get the Darkness Gemstone
Get eternal life
Find all Stage 5 NPCs
Defeat Prius
Defeat Prius in Stage 5 and sustain no damage
Get to the last checkpoint in Stage 5
Get Blood Potion
Defeat Dh'raza and sustain no damage
Don't kill any monsters in any Stage
Get alchemist's heart
Find all Stage 4 NPCs
Defeat the door guardians and sustain no damage
Get Ice Fire Potion
Defeat Firhaz and sustain no damage
Find all Stage 3 NPCs
Find all Stage 2 NPCs
Get Thunder Potion
Defeat Arcadio and sustain no damage
Get Fäy
Kill all the monsters in any Stage
Find all Stage 1 NPCs
Defeat Prius and sustain no damage
Earn an extra life by achieving a score of 10,000
Fall to Reversee