Upon re-entering Akademeia, it becomes immediately apparent that things are not right. From the Main Gate, head to the Fountain Courtyard. Roaming around the courtyard is a Rursan Reaver. If you manage to kill it without being killed yourself, the Rursan Reaver will just resurrect and try to kill you again. Avoid it for now and move on.
Before you head through the north doors to reach the Entrance, you can head to the Airship Landing to find a couple more Knowing Tags. Once you go through the doors to the Entrance, you won’t be able to leave again, so grab the Knowing Tags now or lose them until you reach this point again on your second playthrough.
Once you reach the Entrance, a cutscene will play. After it completes, enter Classroom Zero and head toward the front of the classroom. After a couple more cutscenes play, head to Central Command and talk to Naghi in the back of the room. Head back out to the Entrance and speak with the Dominion Tribune in the center of the room, then re-enter Central Command and speak with Naghi again.
There’s a lot going on in Akademeia that needs to be sorted out before Class Zero can move on to their final Mission. After speaking with Naghi, head back to Classroom Zero and speak with Queen at the front of the room. You’ll be transferred to the Altocrystarium during the conversation with Queen. Once the cutscene is over, take this last opportunity to use the Altocrystarium to power up your spells; once you leave Akademeia you won’t be coming back.
Head back to the Entrance and approach Celestia, the Concordian l’Cie who is standing in front of the doors leading back out to the Fountain Courtyard. Once the cutscene concludes, if you talk to her again she will take Class Zero to their final Mission. You won’t be able to use Eidolons or the Vermilion Bird Squad Command while you’re on this last Mission. Refrain from speaking with her until you’re fully prepared; once you leave Akademeia there’s no turning back.
Head into Central Command, the Crystarium, and Classroom Zero, talk to everyone with the green exclamation points, and then prepare your team for battle. You’re going to want to make sure that most, if not all, of your party members have access to elemental attacks or magic, and a second ability without an element. You’ll need both for certain parts of the final Mission.
Once you’ve finished your preparations, talk to Celestia again and tell her to take you to Pandæmonium.