Here is the full list of all 51 Crystal Project achievements.
Beat the game.
Teleport to an unknown world.
Acquire every Summon.
Acquire a Summon.
Master the Samurai class.
Master the Aegis class.
Obtain an Owl companion.
Obtain a Salmon companion.
Obtain an Ibek companion.
Master the Reaper class.
Learn a Monster Magic spell.
Teleport to a far away land.
Discover every Crystal.
Obtain a Quintar companion.
Discover 12 Crystals.
Discover 7 Crystals.
Open 100 treasure chests.
Conquer the trials.
Defeat 5 boss flames.
Discover 3 Crystals.
Open 50 treasure chests.
Defeat a boss flame.
Defeat 25 boss flames.
Learn every Monster Magic spell.
Change a party member's name.
Change a party member's gender.
Open 500 treasure chests.
Have a party member reach max level.
Breed a Golden Quintar.
Beat the game's secret last boss.
Master the Warrior class.
Master the Monk class.
Master the Rogue class.
Master the Cleric class.
Master the Wizard class.
Master the Warlock class.
Master the Fencer class.
Master the Shaman class.
Master the Scholar class.
Master the Hunter class.
Master the Chemist class.
Master the Ninja class.
Master the Nomad class.
Master the Dervish class.
Master the Beatsmith class.
Master the Assassin class.
Master the Valkyrie class.
Master the Summoner class.
Master the Beastmaster class.
Master the Weaver class.
Master the Mimic class.