Here is the full list of all 58 Final Fantasy IV (3D Remake) achievements. It takes around 80-100 hours to unlock all of the achievements on Windows.
You finished the game twice.
You obtained all augments.
You completed the entire Bestiary.
You defeated Proto-Babil.
You earned all achievements.
You defeated Geryon.
You acquired all hidden summons.
You obtained all the Onion items.
You obtained Adamant Armor.
You talked to everybody in the Developers' Office.
You acquired all summons.
You played through all Namingway events.
You traveled across the entire map.
You obtained 20 augments.
You obtained Ragnarok, Holy Lance, Murasame, and Ribbon.
You finished the game on Hard difficulty.
You finished the game.
You obtained Excalibur.
You earned 500,000 gil.
You defeated the CPU.
You defeated the elemental archfiends.
You raised Cecil (Paladin) to level 70.
You went to the moon on The Lunar Whale.
You defeated Demon Wall.
You defeated 2,000 enemies.
You completed 60% of the Bestiary.
You defeated Rubicante.
You earned 200,000 gil.
You defeated Dr. Lugae.
You raised Cecil (Paladin) to level 50.
You defeated Calcabrina.
You defeated Barbariccia.
You defeated the Magus Sisters.
You earned 50,000 gil.
You raised Cecil (Paladin) to level 30.
You defeated Dark Elf.
You defeated 1,000 enemies.
You completed 30% of the Bestiary.
You defeated Cagnazzo.
You raised Cecil (Paladin) to level 20.
You raised Cecil (Paladin) to level 10.
You defeated Scarmiglione.
You raised Cecil (Dark Knight) to level 25.
You were shipwrecked by Leviathan.
You earned 10,000 gil.
You defeated Mom Bomb.
You defeated 500 enemies.
You defeated the Sahagin that attacked at Kaipo.
You raised Cecil (Dark Knight) to level 20.
You traveled to Damcyan Castle.
You completed 10% of the Bestiary.
You defeated 100 enemies.
You raised Cecil (Dark Knight) to level 15.
You obtained one augment.
You acquired one summon.
You traveled to Mist.
You talked to everybody in the Training Classroom.
You played a new game.