Here is the full list of all 26 The Legend of Heroes: Trails in the Sky the 3rd achievements.
Complete Chapter 1.
Complete the Prologue.
Complete Chapter 2.
Complete Chapter 3.
Complete Chapter 4.
Complete Chapter 5.
Complete Chapter 6.
Complete Chapter 7.
Complete Chapter 8.
Complete all Star Doors.
Complete all Moon Doors.
Complete all Sun Doors.
Complete the Farewall Arena on Nightmare.
Complete "Who Wants to Be a Mirannaire?" Maniac mode.
Complete all minigames on any difficulty.
Defeat all Abyss fiends.
Read all of the books in the Garden.
Read a book you wish you hadn't...
Obtain a special quartz from brave deeds.
Obtain a special quartz from cowardly deeds.
Finish the game on Easy or above.
Finish the game on Normal or above.
Finish the game on Hard or above.
Finish the game on Nightmare.
Beat the ultimate opponent on the highest difficulty.
Carefully examine nearly every chest that you come across before the final chapter.