Upon returning to Akademeia after defeating Qator in the previous mission, you will find the place in shambles and there are dead bodies scattered around. Loot the items on the ground, all of which are Knowing Tags , then head to the Fountain Courtyard, where you will encounter an unknown enemy. There isn't anything you can do for now, so just listen to the dialogue until you can move around freely.
There will be a few Knowing Tags in the Fountain Courtyard, as well as a few more in the Entrance area. To continue, you will need to head to Classroom Zero for a cutscene, then walk to the front of the room for another. Following that, go to Central Command and speak with Naghi, then go to the Entrance area and talk with the Tribune and once more with Naghi back at Central Command.
Return to Classroom Zero and chat with Queen, who will bring you to the Altocrystarium for another cutscene. Upon returning to the Entrance area, you will see Celestia standing near the exit to Fountain Courtyard. Speak with her once, then you'll be able to speak to her any time after that to begin the final mission.
Note: You are free to do the Free Time quests now, so make sure you do it before agreeing to go with Celestia to start the final story mission.