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