Here is the full list of all 55 Tokyo Xanadu eX achievements.
Clear after story -From Here on Out-
Obtain all information on book page in NiAR.
Max out Kou's "Wisdom, Courage, Virtue".
Clear epilogue -A Legend is Born-
Use X-Drive 100 times.
Complete all side-quests.
Clear final chapter -Endless Night-
Forge an unbreakable bond with Asuka.
Forge an unbreakable bond with Rion.
Forge an unbreakable bond with Shio.
Forge an unbreakable bond with Jun.
Forge an unbreakable bond with Towa.
Defeat 500 foes with Critical hits.
Rack up 100 Aerial kills.
Clear chapter 7 -Hollow Quake-
Use X-Strike 100 times.
Defeat 2000 Greeds.
Use EX Skill 300 times.
Fully furnish Kou's room.
Get through a stage without taking any damage.
Use Strike Chain 50 times.
Qualify for the fast clear time bonus in any stage.
Clear chapter 6 -Wing and a Prayer-
Chain Kill 100 times.
Traverse 100,000 meters.
Inflict over 5000 points of damage.
Clear the intermission -Coming of Summer-
Clear chapter 5 -Hidden in the Fog-
Defeat 1000 Greeds.
Pick the most fortuitous...fortune.
Clear chapter 4 -BLAZE: Firestorm of Memories-
Defeat 500 foes with Elemental kills.
Clear chapter 3 -Word of God-
Clear chapter 2 -Mysteries-
Perform a 200+ hit combo.
Defeat 100 Greeds.
Clear chapter 1 -The Eclipse-
Obtain an S rank in any stage.
Wander into the mysterious place of wonder.
Obtain all achievements.
Clear all stages with an S rank.
Obtain all information on friend page in NiAR.
Open all treasure chests.
Clear the game on Infinity difficulty.
Obtain all information on battle page in NiAR.
Obtain all information on recipe page in NiAR.
Obtain every single master core.
Amass a 500,000 yen fortune.
Forge an unbreakable bond with Sora.
Forge an unbreakable bond with Yuuki.
Forge an unbreakable bond with Mitsuki.
Forge an unbreakable bond with Shiori.
Forge an unbreakable bond with Ryouta.
Forge an unbreakable bond with Gorou.
Clear the After Story on Calamity difficulty.