Here is the full list of all 31 FINAL FANTASY III achievements. It takes around 15-20 hours to unlock all of the achievements on Windows.
Earned all achievements.
Completed 100% of the Bestiary entries.
Collected treasure from 100% of the chests.
Traveled to all the map locations.
Defeated the Cloud of Darkness and restored peace to the world.
Defeated Xande and entered the world of darkness.
Obtained all weapons sealed in Eureka.
Obtained all hidden items.
Received power from the Earth Crystal.
Learned all summon magic.
Obtained 500,000 gil.
Awoke Unei with Noah's Lute.
Defeated Garuda and saved Saronia.
Collected treasure from 50% of the chests.
Completed 50% of the Bestiary entries.
Received power from the Water Crystal.
Obtained 100,000 gil.
Defeated 500 monsters.
Received power from the Fire Crystal.
Defeated 300 monsters.
Prevented the destruction of the Tower of Owen.
Completed 10% of the Bestiary entries.
Defeated 100 monsters.
Reached level 50 for all party members.
Smashed the boulder and cleared the path.
Obtained 10,000 gil.
Collected treasure from 10% of the chests.
Leveled up one job to level 50.
Leveled up one job to level 99.
Leveled up one job to level 10.
Received power from the Wind Crystal.