Here is the full list of all 13 JackQuest: The Tale of The Sword achievements.
Kill 50 monsters
Impaled first time
Find a secret room
My first heart
My first gem
Kill Slime without suffering damage
Kill Spider without suffering damage
Kill King without suffering damage
Kill Serpent without suffering damage
Collect all gems
Collect all hearts
Redeem Nara
Defeat Korg without gem and extra heart