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.
Initiated 300 advantage encounters (including double and triple advantage).
Won 600 battles.
Opened every treasure chest.
Completely filled the battle section in the notebook.
Completely filled the books section in the notebook.
Completely filled the character section in the notebook.
Completed all quests, both at the branch campus and during field exercises.
Collected all radio material and reported it to Munk.
Achieved an academy grade of Prestigious.
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 Sara.
Forged a strong bond with Gaius.
Forged a strong bond with Machias.
Forged a strong bond with Laura.
Raised any two characters to Link Level 5.
Completely filled the recipe section in the notebook.
Gathered all 28 varieties of master quartz.
Forged a strong bond with Elise & Alfin.
Forged a strong bond with Towa.
Forged a strong bond with Fie.
Forged a strong bond with Millium.
Forged a strong bond with Emma.
Forged a strong bond with Jusis.
Forged a strong bond with Elliot.
Forged a strong bond with Alisa.
Forged a strong bond with Ash.
Forged a strong bond with Kurt.
Forged a strong bond with Altina.
Forged a strong bond with Juna.
Took all landscape photos and reported them to Vivi.
Acquired over a million mira.
Completely filled the cards section in the notebook.
Used Rush in battle 100 times.
Used Burst in battle 50 times.
Inflicted Break over 800 times.
Earned an S-Rank on any chapter.
Completed the game on nightmare difficulty.
Completed the final chapter.
Completed Chapter 4.
Forged a strong bond with Musse.
Raised a master quartz to level 7.
Completed Chapter 3.
Completed Chapter 2.
Won 100 battles.
Used over 500 follow-up attacks in battle.
Completed Chapter 1.
Used 100 S-Crafts in battle.
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.