Pryde Leads the X-Men

This deck uses the excellent X-Men support structure to allow Kitty to phase/confuse lock the villain while using a rotating cast of cheap allies to handle whatever she can't.

The three key cards in this strategy are Phased and Confused and Mutant Education. Put Phased and Confused on the villain, flip down when they're confused, then send Phased and Confused back into your deck with Mutant Education.

Since you'll be flipping a lot, you can make excellent use of Moira MacTaggert, Kitty's Room, X-Bunker, and X-Mansion for card draw and healing. When you start your turn in Alter-Ego, you can often get to a hand of eight or nine cards, depending on what you've picked for Specialized Training. I usually go for Combat Specialist or Surveillance Specialist, but the villain and modular sets should guide your choice. In a scenario with a lot of minions you may want to go for one of the others.

With Uncanny X-Men out, all your allies are even cheaper. I've avoided the expensive ones to allow Kitty to play more of her strong identity specific cards, which can be a bit pricey but give good to excellent value. Deft Focus and X-Gene will help get them played. Uncanny X-Men and Team Training will also help your allies stick around longer.

Between Phased and Confused, Kitty's Phased mass form, and your numerous allies, you shouldn't be taking too much damage, and what damage you take should be manageable with Kitty's Room and X-Mansion.

If you want to change things up, Team Training and one or two allies can be cut to make room for Weapon X, Cerebro, or more side schemes. (Build Support can be useful, but Superpower Training isn't that strong for Kitty unless you're up against a lot of guard, patrol, and crisis.) You could also put in Danger Room and Danger Room Training, though that makes Team Training awkward unless you also put in Honorary X-Men to keep Kitty an X-Man when she's in alter-ego. If you go down that route you may also be able to make room for Game Time to make even more use of your beefier allies by cutting a couple of resource generators. Those help, but with stronger allies they're less vital.

Another card to consider is Hope Summer. She's not natively an X-Man but her card text makes her one and she can pick up Phased and Confused from your deck, but you'll be hard pressed to play both on the same turn unless you're already well set up.