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