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