Here is the full list of all 38 Pier Solar and the Great Architects trophies - there are 24 bronze, 8 silver, 5 gold and 1 platinum.
Received all trophies.
Won your first battle.
Used an ability that requires level 5 gather.
Enriched your knowledge by doing tutorials.
Helped a hunter in his rabbit hunt.
Finished professor Myer's trials.
Defeated the cave guardian.
Defeated the giant spider.
Defeated the Crab at the sanctuary.
Defeated Ryan the lion.
Defeated the Metal Robot at Timpo factory.
Defeated Ironhart.
Defeated the bakery chef.
Defeated Sasheer.
Defeated the monster living in Teusa.
Defeated the Ludon excavation guardian.
Defeated Kleoneo.
Defeated Cliboe.
Defeated Bethina.
Solve the puzzle in Alina's dream on your first attempt.
Did not give up on hope and fought for a better future.
Gave up on hope and sacrificed yourself for a better future for your friends.
Unlocked the sound test.
Won 100 battles.
Helped the bounty hunter to retrieve his treasure.
Found all spells that can be learned.
Completed Arburus side-quest.
Mastered the slippery game.
Found all master keys.
Found all Sega Genesis cartridges.
Bought all items available in the shops.
Discovered a fragment of another world in yours.
Won 300 battles.
Became a slippery game god.
Collected all the treasures from all chests.
Completed the game fighting only the mandatory battles.
Equipped the best possible items on your characters.
Won 600 battles.