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