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cracks knuckles
Alrighty, first thing's first.
Generally speaking, the two most important things to do are be level 99, and keep yourself buffed.
For level grinding, head into Mementos during Flu Season and farm The Reaper, the effect that particular weather has on Mementos is randomly despairing enemies at the start of a fight, so the Reaper will just die after three turns if he's inflicted with it. If he doesn't get afflicted, just run and re-fight him until it works. Takes about an hour or so if you're unlucky.
For buffs, bring Debilitate for sure. It's a bit of a rare skill on Joker, but if you do Reaper grinding with Crow then he'll actually get that as one of his last skills, and it's an absolute godsend.
Party-wise, you could probably safely bench Mona. Queen has more survivability, and at level 99 their healing is practically the same save for status effects, and those aren't too much of a problem against the twins so you don't lose much by benching him. Be sure to constantly have Queen's defense buff up to mitigate damage even further, on top of Crow's Debilitate.
So, I can safely suggest Queen and Crow as party members. Your fourth slot is mostly flexible, but I'd suggest picking between Skull, Panther, or Noir. Skull brings damage and attack buffs, Panther brings damage and secondary healing if you're worried about Queen's SP, and Noir can bring Heat Riser along with other utility skills like reflects, or some additional damage with Triple Down. I personally ran through with Noir.
Lastly, I highly suggest bringing Yoshitsune with you for damage. The damage from Hassou Tobi is downright nutty, and since it damages both twins you won't have to worry about them reviving each other. If one twin stays dead for too long, her sister will revive her so keep their HP relatively even up until the end.
All-in-all, the fight is less puzzle-like than other series super bosses. You have to sort of think on the fly, and be ready for things to go wrong. Also having evolved Personas for your party (minus Crow ofc) can help to prevent a team wipe. Be sure to keep your buffs/debuffs up, and keep the 50 turn limit in mind, and you should be golden.