Here is the full list of all 25 Epic Quest of the 4 Crystals achievements.
Complete the first stage with Platinum Ranking.
Play a New Game for 1 hour.
Complete the quest "Rats in the Basement".
Collect all 12 Uber Rare Accessories.
Finish Loras’s tasks.
Acquire 2000 Points.
Complete the quest "Moving On".
Acquire the Scuba Mask.
Complete the game.
Defeat 25 enemies.
Defeat 200 enemies.
Defeat 400 enemies.
Play a New Game for 5 hours.
Play a New Game for 10 hours.
Complete the second stage with Platinum Ranking.
Complete the third stage with Platinum Ranking.
Complete the fourth stage with Platinum Ranking.
Complete the fifth stage with Platinum Ranking.
Complete the sixth stage with Platinum Ranking.
Complete the seventh stage with Platinum Ranking.
Complete the ninth stage with Platinum Ranking.
Complete the tenth stage with Platinum Ranking.
Complete the eleventh stage with Platinum Ranking.
Complete the twelfth stage with Platinum Ranking.
Complete the thirteenth stage with Platinum Ranking.