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.
Collected treasure from 100% of the chests.
Completed 100% of the Bestiary entries.
Learned all summon magic.
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.
Reached level 50 for all party members.
Awoke Unei with Noah's Lute.
Obtained 500,000 gil.
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.
Received power from the Fire Crystal.
Prevented the destruction of the Tower of Owen.
Leveled up one job to level 99.
Defeated 500 monsters.
Defeated 300 monsters.
Leveled up one job to level 50.
Completed 10% of the Bestiary entries.
Obtained 10,000 gil.
Smashed the boulder and cleared the path.
Collected treasure from 10% of the chests.
Defeated 100 monsters.
Leveled up one job to level 10.
Received power from the Wind Crystal.