Here is the full list of all 55 Tokyo Xanadu eX achievements.
Clear after story -From Here on Out-
Use X-Drive 100 times.
Clear epilogue -A Legend is Born-
Clear final chapter -Endless Night-
Use EX Skill 300 times.
Fully furnish Kou's room.
Forge an unbreakable bond with Asuka.
Forge an unbreakable bond with Sora.
Forge an unbreakable bond with Shio.
Forge an unbreakable bond with Yuuki.
Forge an unbreakable bond with Shiori.
Forge an unbreakable bond with Rion.
Rack up 100 Aerial kills.
Use X-Strike 100 times.
Defeat 500 foes with Critical hits.
Clear chapter 7 -Hollow Quake-
Chain Kill 100 times.
Defeat 2000 Greeds.
Use Strike Chain 50 times.
Clear chapter 6 -Wing and a Prayer-
Inflict over 5000 points of damage.
Traverse 100,000 meters.
Clear the intermission -Coming of Summer-
Qualify for the fast clear time bonus in any stage.
Clear chapter 5 -Hidden in the Fog-
Defeat 1000 Greeds.
Clear chapter 4 -BLAZE: Firestorm of Memories-
Defeat 500 foes with Elemental kills.
Clear chapter 3 -Word of God-
Clear chapter 2 -Mysteries-
Defeat 100 Greeds.
Perform a 200+ hit combo.
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.
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.
Get through a stage without taking any damage.
Forge an unbreakable bond with Mitsuki.
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 the After Story on Calamity difficulty.