Here is the full list of all 15 The Princess' Heart achievements.
Complete one side-quest.
Complete five side-quests.
Complete ten side-quests.
Get Splendora to join your party.
Acquire 5000 Gold.
Acquire 200,000 Gold.
Defeat Yatmal-Sadag, Demon of Deceit.
Defeat Tanhal-Arag, Demon of Loneliness.
Defeat Xainal-Tarag, Demon of Apostasy.
Defeat Siddal-Vicag, Demon of Cruelty.
Defeat Izdul-Kalag, Demon of Desire.
Play one New Game for 1 hour.
Play one New Game for 10 hours.
Play one New Game for 15 hours.
Finish the game!