Here is the full list of all 16 Legend of the Skyfish trophies - there are 5 silver, 10 gold and 1 platinum.
Get all other trophies.
Defeat the boss of the 3rd campaign.
Defeat 5 of each enemy species found on the Arid Seabed.
Defeat the boss of the 2nd campaign.
Defeat 5 of each enemy species found on the Mamachi Swamp.
Find half of all the secret chests.
Defeat the boss of the 1st campaign.
Defeat 5 of each enemy species found on the Western Ruins.
Defeat 5 enemies using traps.
Beat any level without getting hit once.
Pull enemies with the hook 10 times.
Open your first chest.
Pull yourself using the hook 10 times.
Use your hook to pull an enemy.
Defeat your first enemy.
Use a hatch to pull yourself with the hook.