Here is the full list of all 53 The Legend of Heroes: Trails of Cold Steel IV (EU) trophies - there are 42 bronze, 8 silver, 2 gold and 1 platinum.
Spent the evening before the final battle with Alisa.
Spent the evening before the final battle with Musse.
Forged a strong bond with Kurt, Ash, Elliot, Machias, Jusis, Gaius, and Crow.
Forged a strong bond with Celine and Duvalie.
Completely filled the character section in the notebook.
Used over 500 follow-up attacks in battle.
Initiated 300 advantage encounters. (Including double and triple advantage)
Won 700 battles.
Reached the true ending.
Completed the finale.
Opened every treasure chest.
Used Brave Order in battle over 100 times.
Used Burst in battle 50 times.
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.
Achieved a Unity Grade of Unbreakable.
Gathered all 5 lost arts quartz.
Opened every trial chest.
Completely filled the books section in the notebook.
Won against all opponents in Pom! Pom! Party!
Gathered all 31 varieties of master quartz.
Completely filled the recipe section in the notebook.
Raised a master quartz to level 10.
Completely filled the cards section in the notebook.
Achieved a Special Ops rank of A0.
Raised any two characters to Link Level 7.
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 Laura.
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.
Spent the evening before the final battle with Emma.
Spent the evening before the final battle with Altina.
Spent the evening before the final battle with Juna.
Completed Eventide.
Completed Act 3.
Inflicted Break over 800 times.
Used Rush in battle 100 times.
Completed Act 2.
Won a battle with a tactical bonus of x3.0 or greater.
Completed Fragments.
Completed Act 1.
Used 100 S-Crafts in battle.
Won 100 battles.
Earned an S-Rank on any act.
Completed the prologue.
Acquired over a million mira.
Infiltrated Orchis Tower.
Mastered Trails of Cold Steel IV and earned every trophy.
Completed the game on nightmare difficulty.
Completely filled the battle section in the notebook. (Besides the Extra category)