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