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