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