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