It’s all down to Kirito vs. Administrator now, and their climactic swordfight doesn’t disappoint. Despite having really long hair and only one arm, Administrator is no slouch in the swordsmanship department. She knows all the Aincrad-style moves Kirito showed Eugeo, plus a few that even Kirito doesn’t know about, and seems to revel in the opportunity to teach an insolent cur from the outside world an abject lesson in submitting to his betters.
Kirito looks like he’s just barely hanging on while Administrator is content to draw out his suffering, but Eugeo, barely hanging onto life, reaches out to Kirito, and they have a little tête-à-tête in which Kirito finally recalls the memories he lost of growing up in Rulid Village with Eugeo and Alice. Eugeo tanks Kirito for his friendship, brotherhood, and love these past few years, then bestows upon him the Blue Rose Sword, which becomes the Red Rose Sword in Kirito’s hand.
Now dual-wielding against a one-armed opponent, Kirito would seem to have the upper hand, but it ends up yet another draw, as in exchange for the increasingly crazed Administrator’s last remaining arm, Kirito loses his right one, while Admin reveals her hair is prehensile and can be used to restrain and strangle Kirito, which she does.
Administrator can’t get over how much insolence she has to contend with in this fight, but as Eugeo says, Kirito is going to keep standing up and dusting himself up as many times as it takes. He manages to cut through Admin’s hair, then delivers a strike to her core that does irreparable damage, forcing her to access a console and beam herself out of there.
Before she gets away, promising she’ll be seeing Kirito again in the real world, a naked, burning Chudelkin jumps onto her, seeking her loving embrace, resulting in a huge fiery explosion. Quite the ignominious end for the ruler of the Underworld…though it’s probably not a true end.
With Admin out of Kirito’s hair, he tries to tend to Eugeo, but it’s way too late for anything other than a tearful goodbye, with Eugeo relaying what he now understands about love being something you give, not something you seek. Both a younger Eugeo and a younger Alice appear in Kirito’s head to announce that while their paths may soon separate, their memories of one another will remain forever.
Just after Eugeo passes away, Kirito gets an “external observer call” from Rath: it’s Colonel Kikuoka and Higa. The control room is under assault, either from the military or some other power that wants their hands on the STL tech. They give Kirito instructions to deliver Alice to some place called the “World’s End Altar”, presumably to complete the process of bringing Kirito back to the real world with his brain in one piece. Asuna is also mentioned. But Kikuoka’s foes have other plans.
They seek to sever the main power line, which will cause a surge that could fry Kirito’s fluctlight, killing him before he can be safely extracted from the Underworld. The line is severed, the surge occurs, and Kirito experiences something akin to a lightning strike, inside of which a blurry image of Asuna from above, fitted out in her SAO regalia. Whether it’s Kirito’s memory or Asuna entering the “game” for the first time, I’ll have to wait until October to find out, when the Alicization saga continues with War of Underworld.