Accel World / Dural: Magisa Garden(2012)

Accel World / Dural: Magisa Garden

Chiaki recently returned from America, enrolling into an all-girls school. Her brother used to tell her stories about a "Snow Black Princess" and her adventures in a magical kingdom before he died. Seeing an opportunity, two of her seniors try to install Brain Burst on her, only to be rejected. Turns out her brother already installed it three years ago on his deathbed, and is an unknowing Avatar.

(Source: TV Tropes)