Accel World, Vol. 11 (light novel‪)‬

The Acceleration Research Society, a mysterious organization maneuvering in secret, makes their headquarters at the top of Tokyo Midtown Tower, where the Archangel Metatron is enshrined. This completely invincible Legend-class Enemy guards the Society from all would-be attackers, and so the Seven Kings meet in order to devise some means to defeat the Enemy and the Acceleration Research Society along with it.
The secret plan they come up with necessitates that Silver Crow gain a new ability, Theoretical Mirror.
Although he's been ordered to obtain this ability--which can withstand even the instant death of Metatron's ultimate laser--abilities require action to trigger their manifestation, in contrast with the way Incarnate techniques are generated through the imagination. Thus, Haruyuki's powerful imagination won't help him this time!

While Haruyuki is stumped at how to even begin this difficult task, Ardor Maiden (a.k.a. Utai Shinomiya) begins relating a sad past...