The game takes place after the events of BlazBlue: Continuum Shift. The Story Mode has three scenarios: Chronophantasma, Sector Seven and Six Heroes.

January, 2200AD
It's been over one week since the loop came to an end.
Having destroyed the Cauldrons, Ragna had finished his quest.

However...
There was still unfinished business in his books.
To defeat his now-revived nemesis, Terumi.
Terumi abducts the Successor of the Azure, Noel, and forces the Master Unit, Amaterasu to appear in the human plane.
Hatred and vengeance awaken the Sword of the Godslayer, Kusanagi (Mu -No.12-).

Ragna sacrifices his own flesh and blood to save Noel, but even that Terumi had predicted.
In a small window of opportunity, Terumi nullifies Takamagahara.

It was all a part of their—
The NOL's highest commanding leader, the Imperator's will.
Later, Kokonoe restores Ragna's flesh...
...and he sets his course for the Federation's Hierarchical City: Ikaruga.
Little did he know, he would encounter the phantoms of time, the Chronophantasma, at his destination.

[From Blazblue Wiki]