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