lusty stratus
This boss is a literal sandbag. You don't have to kill him, just do what the side missions tell you to. You can run 6 dolls.
Stab breaking is easy, but what about the missions regarding phase weakness?
The boss does NOT have any natural phase weaknesses. After getting hit by a phase element, gain the weakness if he doesn't have it, otherwise lose it.
Your goal should be to break stability. After stab break, kill the fortresses he spawns and he'll gain all weaknesses. Lotta and Klukai are most efficient, but not required at all. Just keep repeating the process until the side missions are complete. Again, you need not complete all in one go. (A cheese you can do is you bring Sabrina and Suomi for forced phase weakness, then spam hit with Tololo and Maki for hydro and ice damage respectively.)
For support attack mission, QJ is best especially right after killing the fortresses. Mosin and Neme and really any support attacker will do.
Lastly, tactical score I have no idea how what all the conditions are. All I know is phase weakness hits score 3 points so just spam those until you get 900 total.
For your team comp you just need a strong AOE that can 2 shot the fortresses, even better if 1 shot. Since this battle is just hitting a sandbag, your units just needs to not die. A team I ran was Tololo, Sabrina, Suomi, Maki, Lotta, Cheeta. I never really had to worry about dying with double healers while Sabrina/Suomi were the phase weakness appliers to Tololo/Maki. Cheeta and Suomi were support attackers, and Lotta was strong enough to 2 shot the fortress. In short, with this team you want someone to AOE down the fortress while farming tactical points by using forced weakness.
Just survive as long as you can with cover and whittle down on the mission objectives.
undone fiber
versed lark
heady leaf
rugged mesa
rapid crow
stuck peak
silk rain
charred crater
sharp notch
brittle briar
limpid loom
devout lake