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