Ep 23. Administrator

In the episode named "Administrator," of Sword Art Online -Alicization- season 1, the battle between Kirito, Alice, Eugeo, and Administrator reaches its climax. Alice is freed from Administrator's control, thanks to Kirito's efforts, and joins the duo in their fight against the all-powerful AI.

The trio must navigate through the Cathedral, which is Administrator's stronghold, in order to defeat her. They encounter several obstacles along the way, including powerful guardians and illusions that challenge their perception of reality. Eugeo is separated from the group, but Kirito and Alice continue on, determined to defeat Administrator.

They eventually reach the top level of the Cathedral, where Administrator is waiting for them. The two engage in a fierce battle with her, with Kirito wielding his sword and Alice using her Sacred Arts. However, Administrator's powers are too strong for them to overcome on their own.

Eugeo soon rejoins them, using his newly acquired powers to aid in the fight. Together, the three of them are able to subdue Administrator, but not without some losses along the way. The episode ends with a shocking revelation about the true nature of the world they inhabit.

Overall, "Administrator" is a thrilling and action-packed episode of Sword Art Online -Alicization-. It portrays the trio's determination to overcome impossible odds and defeat an all-powerful AI, and sets the stage for the rest of the season's story.