Here is the full list of all 53 The Legend of Heroes: Sen no Kiseki IV -THE END OF SAGA- achievements.
Completely filled the battle section in the notebook. (Besides the Extra category)
Completed the finale.
Completely filled the character section in the notebook.
Opened every treasure chest.
Raised any two characters to Link Level 7.
Raised a master quartz to level 10.
Achieved a Special Ops rank of A0.
Achieved a Unity Grade of Unbreakable.
Gathered all 31 varieties of master quartz.
Completely filled the cards section in the notebook.
Completely filled the recipe section in the notebook.
Completed all quests.
Gathered all 5 lost arts quartz.
Opened every trial chest.
Completely filled the fishing section in the notebook. (All 30 types of fish + Rod Lv. Max)
Took all landscape photos and reported them to Rex.
Completely filled the books section in the notebook.
Won against all opponents in Pom! Pom! Party!
Spent the evening before the final battle with Sara.
Spent the evening before the final battle with Emma.
Spent the evening before the final battle with Laura.
Spent the evening before the final battle with Alisa.
Completed Eventide.
Spent the evening before the final battle with Juna.
Completed Act 3.
Inflicted Break over 800 times.
Completed Act 2.
Used over 500 follow-up attacks in battle.
Won a battle with a tactical bonus of x3.0 or greater.
Completed Fragments.
Completed Act 1.
Used 100 S-Crafts in battle.
Won 100 battles.
Used Brave Order in battle over 100 times.
Earned an S-Rank on any act.
Completed the prologue.
Infiltrated Orchis Tower.
Earned all achievements.
Completed the game on nightmare difficulty.
Acquired over a million mira.
Won 700 battles.
Initiated 300 advantage encounters. (Including double and triple advantage)
Used Rush in battle 100 times.
Used Burst in battle 50 times.
Spent the evening before the final battle with Altina.
Spent the evening before the final battle with Musse.
Spent the evening before the final battle with Fie.
Spent the evening before the final battle with Towa.
Spent the evening before the final battle with Elise.
Spent the evening before the final battle with Alfin.
Forged a strong bond with Celine and Duvalie.
Forged a strong bond with Kurt, Ash, Elliot, Machias, Jusis, Gaius, and Crow.
Reached the true ending.