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