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