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.
Defeated Zeromus and restored peace to the world.
Collected treasure from 100% of the chests.
Obtained all sealed equipment.
Reached level 70 for all party members.
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.
Climbed Mt. Ordeals and became a paladin.
Defeated 500 monsters.
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.