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