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