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