Here is the full list of all 38 Rune Factory: Tides of Destiny (EU) trophies - there are 21 bronze, 12 silver, 4 gold and 1 platinum.
Earn all trophies.
Achieve repeat victories in the colloseum.
Win a battle in the colloseum.
Earn the goodwill of many residents on Fenith Island.
Raise all of the islands out of the sea.
Defeat 5000 monsters.
Successfully salvage 30 times.
See the true face of the man in the mask.
Defeat the Legendary Golem.
Lift the stone curse from the Flame Spirit Shrine.
Lift the stone curse from the Earth Spirit Shrine.
Lift the stone curse from the Water Spirit Shrine.
Find out what's wrong with the Plant Golem and get him working again.
Catch a cold 100 times.
Consume 100 recovery drinks.
Successfully salvage 20 times.
Successfully land 2000 fish.
Defeat 30 giant monsters.
Defeat 20 giant monsters.
Successfully land 1000 fish.
Defeat 3000 monsters.
Defeat 10 giant monsters.
Successfully salvage 10 times.
Listen to Maerwen's explanation about trophies.
Perform a double-jump 500 times.
Defeat 1500 monsters.
Successfully land 300 fish.
Defeat 500 monsters.
Successfully land a fish.
Defeat 100 monsters.
Get to the bottom of why Sprout Island turned to stone.
Successfully craft 1500 items.
Successfully craft 800 items.
Successfully craft 300 items.
Successfully craft an item.
Stay awake until you collapse at 5AM.
Fail at cooking one time.
Use the Plant Golem to raise an island out of the sea.