Here is the full list of all 53 The Legend of Heroes: Trails of Cold Steel III achievements.
Mastered Trails of Cold Steel III and earned every achievement.
Completely filled the battle section in the notebook.
Completely filled the character section in the notebook.
Completed the game on nightmare difficulty.
Opened every treasure chest.
Completed all quests, both at the branch campus and during field exercises.
Completely filled the books section in the notebook.
Achieved instructor rank S.
Forged a strong bond with Towa.
Forged a strong bond with Millium.
Forged a strong bond with Machias.
Completely filled the recipe section in the notebook.
Achieved an academy grade of Prestigious.
Won 600 battles.
Raised any two characters to Link Level 5.
Acquired over a million mira.
Completed the final chapter.
Initiated 300 advantage encounters (including double and triple advantage).
Gathered all 28 varieties of master quartz.
Completed Chapter 4.
Collected all radio material and reported it to Munk.
Completely filled the fish section in the notebook. (All 25 types of fish + Rod Lv. Max)
Forged a strong bond with Jusis.
Forged a strong bond with Emma.
Forged a strong bond with Laura.
Forged a strong bond with Elliot.
Forged a strong bond with Ash.
Forged a strong bond with Alisa.
Forged a strong bond with Fie.
Forged a strong bond with Sara.
Forged a strong bond with Juna.
Forged a strong bond with Elise & Alfin.
Forged a strong bond with Altina.
Forged a strong bond with Kurt.
Forged a strong bond with Gaius.
Forged a strong bond with Musse.
Completely filled the cards section in the notebook.
Took all landscape photos and reported them to Vivi.
Used Burst in battle 50 times.
Completed Chapter 3.
Raised a master quartz to level 7.
Inflicted Break over 800 times.
Completed Chapter 2.
Used Rush in battle 100 times.
Used over 500 follow-up attacks in battle.
Used 100 S-Crafts in battle.
Completed Chapter 1.
Earned an S-Rank on any chapter.
Won 100 battles.
Used Brave Order in battle over 100 times.
Won a battle with a tactical bonus of x3.0 or greater.
Completed the prologue.
Completed the orienteering exercise.