This is available after getting Laharl.
After this achievement, there will be a new bill in the Senate, Destroy the Root of All Evil!
. Pass that bill and the post-game chapter will open.
If you're coming to this directly after Laharl, prepare to get clobbered. Asagi uses the same trick you should when powerleveling in the form of dual wielding fused magichange. Even around level 5000, if your equipment isn't up to snuff, she will still one shot you.
However, the earliest you can possibly do this is with a level 4000 Fenrich and Desco with four Beast Masters. Note that this strategy will likely take several attempts to work due to low hit rates.
Use Desco to to nuke the gunners, then have an unnecessary character like Axel toss her back into the base panel. End the turn and let the Bio-Suits come closer. Repeat the process with the bio-suits and bait Asagi into getting closer to the base panel.
Once she's close enough, it's showtime. Bring Desco out and get her fused, then surround her with Beast Masters. Get a Fighter to use Fight Shot, and you'll immediately see the issue with this strategy: Yog Sothoth has a 12% chance to hit. However, you'll need at least one to hit for about half a million damage in order for this to work.
Involving less strategy is Fenrich. Buff him with Fight Shot and have Valvatorez and Artina stand next to him for another stat boost. He has a 33% chance to hit, but this is a bit more reliable.
After both damage runs, use another throwaway character to lift Asagi, then end turn. That character will take 600k damage and most likely die, but it prevents her from attacking. This effectively adds a timer to the stage of how many times you can deploy a throwaway to prevent her attack, but it is still possible to finish her off before you only have Desco and Fenrich left.