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