Here is the full list of all 31 FINAL FANTASY III trophies - there are 16 bronze, 8 silver, 6 gold and 1 platinum.
Earned all trophies.
Defeated the Cloud of Darkness and restored peace to the world.
Completed 100% of the Bestiary entries.
Collected treasure from 100% of the chests.
Defeated Xande and entered the world of darkness.
Traveled to all the map locations.
Learned all summon magic.
Obtained all weapons sealed in Eureka.
Obtained all hidden items.
Reached level 50 for all party members.
Received power from the Earth Crystal.
Leveled up one job to level 99.
Awoke Unei with Noah's Lute.
Obtained 500,000 gil.
Defeated Garuda and saved Saronia.
Collected treasure from 50% of the chests.
Completed 50% of the Bestiary entries.
Received power from the Water Crystal.
Leveled up one job to level 50.
Received power from the Fire Crystal.
Obtained 100,000 gil.
Defeated 500 monsters.
Prevented the destruction of the Tower of Owen.
Defeated 300 monsters.
Completed 10% of the Bestiary entries.
Smashed the boulder and cleared the path.
Collected treasure from 10% of the chests.
Leveled up one job to level 10.
Obtained 10,000 gil.
Defeated 100 monsters.
Received power from the Wind Crystal.