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.
Raised a master quartz to level 10.
Completed all quests.
Completely filled the fishing section in the notebook. (All 30 types of fish + Rod Lv. Max)
Took all landscape photos and reported them to Rex.
Completely filled the books section in the notebook.
Gathered all 5 lost arts quartz.
Opened every trial chest.
Achieved a Special Ops rank of A0.
Won against all opponents in Pom! Pom! Party!
Gathered all 31 varieties of master quartz.
Completely filled the cards section in the notebook.
Spent the evening before the final battle with Altina.
Completed Eventide.
Completed Act 3.
Completed Act 2.
Used over 500 follow-up attacks in battle.
Used Burst in battle 50 times.
Completed Fragments.
Used Brave Order in battle over 100 times.
Completed Act 1.
Earned an S-Rank on any act.
Used 100 S-Crafts in battle.
Won 100 battles.
Won a battle with a tactical bonus of x3.0 or greater.
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.
Opened every treasure chest.
Completely filled the battle section in the notebook. (Besides the Extra category)
Completely filled the character section in the notebook.
Completely filled the recipe section in the notebook.
Acquired over a million mira.
Won 700 battles.
Initiated 300 advantage encounters. (Including double and triple advantage)
Inflicted Break over 800 times.
Raised any two characters to Link Level 7.
Used Rush in battle 100 times.
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 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.