Sword Art Online 13 (light novel)

Following a mighty clash, Kirito and Eugeo find themselves separated for the last leg of their journey to the top of Central Cathedral. Kirito, forced into an unlikely alliance with Alice the Integrity Knight, continues his climb from the outside, while trying not to fall to his death. At the same time, Eugeo must face off against the Integrity Knight Commander himself, Bercouli Synthesis One! Although the journey is nearing its end, they'll soon learn that the cathedral is still full of surprises...