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