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