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.
Exchanged the pink tail for Adamant Armor.
Completed 100% of the Bestiary entries.
Reached level 70 for all party members.
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.
Obtained all hidden items.
Defeated the four elemental lords again.
Learned all non-secret summon magic.
Obtained Excalibur.
Obtained the Lunar Whale and landed on the moon.
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.