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