Here is the full list of all 51 The Legend of Heroes: Trails of Cold Steel (EU) trophies - there are 38 bronze, 10 silver, 2 gold and 1 platinum.
Mastered Trails of Cold Steel and earned every trophy.
Completed the game on nightmare difficulty.
Completed the game on hard or nightmare difficulty.
Forged a strong bond with Jusis.
Forged a strong bond with Laura.
Forged a strong bond with Elliot.
Forged a strong bond with Alisa.
Completed all of the character profiles in the notebook.
Played for over 100 hours.
Acquired over a million mira.
Completely filled the book section of the notebook.
Forged a strong bond with Machias.
Forged a strong bond with Fie.
Forged a strong bond with Gaius.
Forged a strong bond with Millium.
Forged a strong bond with Crow.
Forged a strong bond with Towa.
Forged a strong bond with Sara.
Gathered all 28 varieties of master quartz.
Canceled enemy arts and crafts 100 times.
Used Burst in battle 50 times.
Won 1000 battles.
Completed the final chapter.
Completely filled the monster guide.
Forged a strong bond with Emma.
Achieved student rank A0.
Opened every treasure chest in a single playthrough.
Acquired the strongest weapon for any character.
Used Rush in battle 100 times.
Completed all quests, both extra-curricular and during field studies.
Obtained all recipes.
Caught all varieties of fish.
Received the Lionheart Medal of Heroism from Principal Vandyck.
Completed Chapter 6.
Used over 500 follow-up attacks in battle.
Completed Chapter 5.
Raised any two characters to Link Level 5.
Raised a master quartz to level 5.
Won 500 battles.
Completed Chapter 4.
Completed Chapter 3.
Initiated 300 advantage encounters (including double and triple advantage).
Used 100 S-Breaks in battle.
Earned an S-Rank on any chapter.
Completed Chapter 2.
Defeated 8 enemies at once.
Won 100 battles.
Completed Chapter 1.
Completed the prologue.
Arrived in Trista for the first day of school.
Won a battle with a tactical bonus of x2.0 or greater.