Continuum Shift Story Thread and jump into Chrono Phantasma with the miniscule amount of story information slipping out of the loke tests!
Amane Nishiki - Upon hearing rumors of a handsome, young vigilante, he sets out to recruit them into his troupe.
Bullet - A mercenary who was once attached to a certain Sector Seven assault team. She's tracking down Kokonoe of Sector Seven to try and unravel the mystery behind the massacre of her comrades.
Azrael - Once sealed away in a prison for commiting a grave crime, this uncontrollable warrior has been deployed to Ikaruga under someone's orders.
Duodecim, Prime Goddess Amaterasu, Six Heroes, Zero-Weave: Izayoi, Cruel Curse, Amplification Squad, Ars Magus Strengthening, Crimson Eyes, God Dance, Illusion of Time (PV 1:04)
Heavenly Cave (PV 3:00)
So, Bullet was presumably hired by Sector Seven to work in the same squad as Tager, and left at some point in the past before they were wiped out in his mission in Ikaruga. Azrael's also under mysterious orders issued by an unknown entity and had apparantly been imprisoned by Sector Seven.
As for the keywords, I think the Amplification Squad may have been mentioned in the NOL military overview, but I don't have all my documents handy to double check. Ars Magus Strengthening is new, I believe, and will probably get a nifty Latin localization when the game's released in English. Crimson Eyes (or more accurately, "crimson magic eyes" or "crimson demon eyes", is speculated to refer to Rachel. No idea about God Dance. Illusion of Time is obviously the literal translation of "Chrono Phantasma". Heavenly Cave is a reference to the cavern that Amaterasu hid in, in Japanese mythology.