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