Here is the full list of all 14 JackQuest: Tale of the Sword trophies - there are 3 silver, 10 gold and 1 platinum.
Obtained all trophies in JackQuest
Redeem Nara
Defeat Korg
Collect all gems
Kill the King boss
Collect all hearts
Kill the Serpent boss
Kill the Spider boss
Kill 50 monsters
My first heart
My first gem
Find a secret room
Kill the Slime boss
Impaled first time