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