In 2046 Japan, where most of daily life occurs online through quantum communication terminals, a girl named Chiaki Chigira returns from the United States to enroll at the all-girls Seibi Academy. Chiaki is driven by the stories her late brother told her about a legendary Burst Linker known as Black Lotus, and she seeks to become strong enough to meet her idol. Upon arriving, she quickly demonstrates her physical prowess and is recruited by the eccentric members of the Mathematics and Martial Arts Research Society, or Enbuken, who reveal the existence of the secretive Brain Burst program. However, when the seniors attempt to install the software, they discover it is already present, installed by Chiaki's brother on his deathbed three years prior without her knowledge. This discovery launches Chiaki into the Accelerated World, where her duel avatar, the rare metal-colored Aluminum Valkyrie, becomes a key asset to the club.

The story is set both in the real world of the Seibi Academy campus and within the various stages of the Accelerated World, primarily following the Enbuken as they grow as Burst Linkers. The club is led by the boisterous and powerful Yuuko Hoori, whose dragon-like avatar is Orange Raptor, alongside her close companion Kurumi Kuruma, who controls Violet Dancer. The group is soon joined by the timid Lilya Usachova, who becomes Chiaki's first close friend in the Accelerated World and whose avatar, Iris Alice, possesses latent, powerful abilities. Together, this group forms a new legion named Skazka Priskazka to compete in the territory wars of Tokyo's accelerated world.

Over the course of the narrative, Chiaki and her friends face multiple significant challenges. An early arc involves a conflict with Vanilla Slicer, a Burst Linker from the rival Seioh Academy, which forces Chiaki to help Lilya overcome her inner weaknesses and unlock a new power. A major turning point occurs when the Enbuken undertakes the Legion Quest, a difficult dungeon exploration in the Unlimited Neutral Field of Ikebukuro, to formally establish their legion. The overarching mystery driving the plot is the legacy of Chiaki's deceased brother, Souya Chigira, a high-level Burst Linker known as Glass Monarch. As Chiaki delves deeper into Brain Burst, she uncovers secrets about his past, his connection to a colorless faction known as Faceless, and the true nature of his fate. The story culminates in a fateful reunion that reveals the truth about her brother and his final intentions for her, bringing Chiaki's journey to fulfill his wish to a close.