Here is the full list of all 53 The Legend of Heroes: Trails of Cold Steel III achievements.
Completely filled the battle section in the notebook.
Mastered Trails of Cold Steel III and earned every achievement.
Opened every treasure chest.
Completed the game on nightmare difficulty.
Completed all quests, both at the branch campus and during field exercises.
Acquired over a million mira.
Completely filled the character section in the notebook.
Initiated 300 advantage encounters (including double and triple advantage).
Forged a strong bond with Juna.
Forged a strong bond with Jusis.
Forged a strong bond with Millium.
Forged a strong bond with Sara.
Forged a strong bond with Gaius.
Forged a strong bond with Machias.
Completed the final chapter.
Completely filled the books section in the notebook.
Used 100 S-Crafts in battle.
Completely filled the recipe section in the notebook.
Achieved an academy grade of Prestigious.
Gathered all 28 varieties of master quartz.
Collected all radio material and reported it to Munk.
Completed Chapter 4.
Achieved instructor rank S.
Forged a strong bond with Laura.
Forged a strong bond with Fie.
Forged a strong bond with Kurt.
Forged a strong bond with Elliot.
Forged a strong bond with Emma.
Forged a strong bond with Alisa.
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 Elise & Alfin.
Forged a strong bond with Altina.
Forged a strong bond with Musse.
Forged a strong bond with Towa.
Took all landscape photos and reported them to Vivi.
Used Burst in battle 50 times.
Won 600 battles.
Completely filled the cards section in the notebook.
Raised any two characters to Link Level 5.
Completed Chapter 3.
Raised a master quartz to level 7.
Completed Chapter 2.
Used over 500 follow-up attacks in battle.
Inflicted Break over 800 times.
Used Brave Order in battle over 100 times.
Used Rush in battle 100 times.
Completed Chapter 1.
Earned an S-Rank on any chapter.
Won 100 battles.
Won a battle with a tactical bonus of x3.0 or greater.
Completed the prologue.
Completed the orienteering exercise.