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.
Defeated the bakery chef.
Used an ability that requires level 5 gather.
Defeated the Metal Robot at Timpo factory.
Defeated the Ludon excavation guardian.
Defeated Ryan the lion.
Won 300 battles.
Solve the puzzle in Alina's dream on your first attempt.
Defeated the monster living in Teusa.
Unlocked the sound test.
Defeated the Crab at the sanctuary.
Won 100 battles.
Defeated the cave guardian.
Won your first battle.
Helped a hunter in his rabbit hunt.
Enriched your knowledge by doing tutorials.
Received all trophies.
Finished professor Myer's trials.
Defeated the giant spider.
Defeated Ironhart.
Defeated Sasheer.
Defeated Kleoneo.
Defeated Cliboe.
Defeated Bethina.
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.
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.
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.