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