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