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.
Found and learned all secret summon magic.
Defeated Zeromus and restored peace to the world.
Completed 100% of the Bestiary entries.
Collected treasure from 100% of the chests.
Obtained all sealed equipment.
Exchanged the pink tail for Adamant Armor.
Traveled to all the map locations.
Obtained all hidden items.
Learned all non-secret summon magic.
Reached level 70 for all party members.
Defeated the four elemental lords again.
Obtained the Lunar Whale and landed on the moon.
Obtained Excalibur.
Defeated Rubicante, the Lord of Fire.
Defeated 1000 monsters.
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 Cagnazzo, the Lord of Water.
Defeated 500 monsters.
Obtained 100,000 gil.
Climbed Mt. Ordeals and became a paladin.
Collected treasure from 10% of the chests.
Obtained 10,000 gil.
Completed 10% of the Bestiary entries.
Defeated 100 monsters.
Accidentally destroyed the village of Mist.