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