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