Here is the full list of all 53 The Legend of Heroes: Trails of Cold Steel IV achievements.
Reached the true ending.
Completed the finale.
Completely filled the recipe section in the notebook.
Opened every trial chest.
Gathered all 5 lost arts quartz.
Completely filled the books section in the notebook.
Won against all opponents in Pom! Pom! Party!
Gathered all 31 varieties of master quartz.
Took all landscape photos and reported them to Rex.
Completely filled the fishing section in the notebook. (All 30 types of fish + Rod Lv. Max)
Achieved a Special Ops rank of A0.
Completely filled the cards section in the notebook.
Raised a master quartz to level 10.
Spent the evening before the final battle with Emma.
Spent the evening before the final battle with Laura.
Spent the evening before the final battle with Juna.
Spent the evening before the final battle with Musse.
Spent the evening before the final battle with Alisa.
Spent the evening before the final battle with Fie.
Spent the evening before the final battle with Sara.
Spent the evening before the final battle with Elise.
Spent the evening before the final battle with Altina.
Spent the evening before the final battle with Alfin.
Completed Eventide.
Spent the evening before the final battle with Towa.
Forged a strong bond with Celine and Duvalie.
Acquired over a million mira.
Completed Act 3.
Raised any two characters to Link Level 7.
Won 700 battles.
Completed Act 2.
Initiated 300 advantage encounters. (Including double and triple advantage)
Used Burst in battle 50 times.
Completed Fragments.
Used Rush in battle 100 times.
Completed Act 1.
Used 100 S-Crafts in battle.
Inflicted Break over 800 times.
Used over 500 follow-up attacks in battle.
Earned an S-Rank on any act.
Used Brave Order in battle over 100 times.
Won a battle with a tactical bonus of x3.0 or greater.
Won 100 battles.
Completed the prologue.
Infiltrated Orchis Tower.
Mastered Trails of Cold Steel IV and earned every achievement.
Achieved a Unity Grade of Unbreakable.
Completed the game on nightmare difficulty.
Completed all quests.
Opened every treasure chest.
Completely filled the battle section in the notebook. (Besides the Extra category)
Completely filled the character section in the notebook.
Forged a strong bond with Kurt, Ash, Elliot, Machias, Jusis, Gaius, and Crow.