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