Here is the full list of all 36 Trials of Proelium achievements.
You defeated Sacratus
You defeated Veneficus
You defeated Phaedra
You defeated Cupide
You defeated Extasis
Completed the quest "The weird fox"
Complete all job advancements
Defeat a boss on chaos mode
You defeated Fire Eldritch
You defeated the lady of the trees
You defeated the ice guardian
You defeated Tukeur Dunya
You collected all books for Sacrista
Learn an ultimate spell
You defeated Leviathan
Catch a rare fish while fishing
Won a rare prize from Gachapon
Training is important
You defeated Lord Crab
Complete the quest "Space bending"
Finish all Squalus quests
Reached max level as Letha or Yoni
You defeated the samurai princess
Found a hidden treasure chest
Found all hidden treasure chests
Complete the quest "Protector of the forest"