Got any advice for Yuyuko and Youmu?
For starters, you'll want a good team. Alice for tanking stuff is obvious. From there, you can go about this in several ways. I like to use Nitori, Patchy, Marisa, and Byakuren.
Formation can either be Speed to get maximum advantage out of Marionetter Parrar or Magician's Circle/Luna Dial if you want to take a more aggressive approach.
Alice should be suited up with +RES boosting accessories and something that resists instant death. She should have Hourai Doll, Marionetter Parrar, and London Dolls for her skills in this fight.
Patchy & Marisa should be armed to do extreme magical damage. Since both Yuyu and Youmu are weak to Fire/Ice/Elec/Earth, choose all your favorite elemental spells for one element for both characters (preferably not Earth since Marisa has no spells in that category as well as Nitori). Patchy should then be set with Active Elemental and whatever field effect skill that boosts the element you choose to spam in this fight.
Nitori should have 20 points in her Gun skill tree (20 points lets her ignore an enemy's chance to Perfect Dodge) and be equipped with a chaser and an attack that match the element you choose for this fight. Elemental Shells skill is a good idea to give her as well.
Byakuren needs Weapon Bless, Hyper Trigger, Unresist, and Starfire equipped. If she's level 21, you can bring in Spell Enhance as well if you'd like.
Should you not choose to use her, Sanae with her +PATK, +MATK, and +RES buffing skills along with a healing spell or two should suffice.
Commander should be Mokou or whomever you'd like. This fight won't last too long if you execute everything correctly.
Now then, battle. Youmu needs to go down fast as her damage is pretty brutal. Yuyu has some fairly weak elemental spells and a few status inflicting moves so you can leave her alone for now.
Alice should open with Hourai Doll while Marisa blasts Youmu with your element of choice, Nitori enchants her weapon with your chosen element, Patchy casts Active Elemental to manipulate for your chosen element or whatever field effect skill she has armed to raise elemental damage for a specific element, and Byakuren casts Hyper Trigger on herself.
Next round, Alice should spam Parrar, Nitori should start attacking Youmu with her best gun skill available or setup a chaser for your chosen element, Marisa keeps up the spell spam on Youmu, Patchy should perform whatever action you didn't do in the first turn, and Byakuren can either buff up Nitori with Weapon Bless or attempt to cast Unresist on Yuyu. By now, Youmu should be getting close to being KO'd if she's not already there.
3rd round, same as always, except Patchy should now start spamming magic and Byakuren should cast Starfire on Yuyu if Unresist is active or buff people up if you failed to get Unresist to connect and it's on cooldown. Youmu should be KO'd at this point.
The purpose of Starfire is to debuff Yuyu's M.Def. Spells that were lucky to hit for double digits can now do several hundred points of damage per cast with buffs active. Nitori's chasers can also wreck Yuyu since the chasers are based on Nitori's P.Atk stat and Yuyu has no P.Def to speak of. That and chasers have 100% accuracy so having 20 points in her Gun skill tree will make doubly sure that no P. Dodge trickery from Yuyu will disrupt them.
Purgatory Impale from Nitori though...oh god that skill. If you've seen my pic from the fight earlier in this thread, then you'll see that it can just obliterate these two with the right buffs and formation.
However, you still have the issue of when Yuyu runs out of HP. She'll perform a final attack that has an extremely high chance to cause instant death to your entire party. There are a ton of ways to get around this though.
Based on this party, you can opt to have Alice use London Dolls on someone the turn you plan to take out Yuyu so that person can survive. You can also set it up so that Yuyu falls due to chaser damage as the final attack will never activate if that happens.
Other options require different party members, but you can have Yuyu fall due to poison damage (Satori's Poison Art skill), Reimu can use her one barrier skill that blocks a certain type of status effect for that turn (Instant Death is a Quick status effect I believe), Sakuya can take out Yuyu if she activates Private Square before dealing the killing blow, and probably one or two other ways I haven't thought of.