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