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.
Completed 100% of the Bestiary entries.
Found and learned all secret summon magic.
Exchanged the pink tail for Adamant Armor.
Obtained all sealed equipment.
Obtained all hidden items.
Reached level 70 for all party members.
Learned all non-secret summon magic.
Obtained Excalibur.
Traveled to all the map locations.
Collected treasure from 100% of the chests.
Defeated the four elemental lords again.
Obtained the Lunar Whale and landed on the moon.
Obtained 500,000 gil.
Defeated Rubicante, the Lord of Fire.
Collected treasure from 50% of the chests.
Completed 50% of the Bestiary entries.
Arrived in the underworld.
Defeated Barbariccia, the Lord of Wind.
Defeated 1000 monsters.
Obtained 100,000 gil.
Defeated Cagnazzo, the Lord of Water.
Climbed Mt. Ordeals and became a paladin.
Defeated 500 monsters.
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.