Here is the full list of all 30 FINAL FANTASY IV achievements. It takes around 20-25 hours to unlock all of the achievements on Windows.
Earned all achievements.
Defeated Zeromus and restored peace to the world.
Exchanged the pink tail for Adamant Armor.
Found and learned all secret summon magic.
Collected treasure from 100% of the chests.
Obtained all hidden items.
Obtained all sealed equipment.
Completed 100% of the Bestiary entries.
Traveled to all the map locations.
Obtained Excalibur.
Defeated the four elemental lords again.
Learned all non-secret summon magic.
Defeated 1000 monsters.
Obtained the Lunar Whale and landed on the moon.
Defeated Rubicante, the Lord of Fire.
Reached level 70 for all party members.
Collected treasure from 50% of the chests.
Obtained 500,000 gil.
Completed 50% of the Bestiary entries.
Arrived in the underworld.
Defeated Barbariccia, the Lord of Wind.
Defeated 500 monsters.
Defeated Cagnazzo, the Lord of Water.
Obtained 100,000 gil.
Climbed Mt. Ordeals and became a paladin.
Collected treasure from 10% of the chests.
Completed 10% of the Bestiary entries.
Obtained 10,000 gil.
Defeated 100 monsters.
Accidentally destroyed the village of Mist.