Phoenix Rising

Ever Vigilant (requires Phoenix Suit for Aerial), What Doesn't Kill Me, and Phoenix Firebird give Phoenix eight two-cost readies along with some healing and thwarting. Telekinetic Shield and Endurance also minimize the number of times she needs a break, so White Hot Room isn't very useful in this deck.

Psychic Misdirection, Pinned Down, Mental Paralysis, and Mind Control all manage minions almost to the point of not caring about them.

Black Widow is here to prevent Shadow of the Past and Burning Hunger (if Phoenix is Unleashed). Protective Training can give Cyclops some extra time out to keep Phoenix's power counters up or to give another player's X-Men ally more rounds of basic actions. Jocasta grabs a Psychic Misdirection out of the discard pile.

Defensive Training has two copies so that once per Alter-Ego turn you can grab some Psychic Misdirection or readying Protection events from discard (9 targets in the deck).

This deck is expensive, but with 16 targets for Team-Building Exercise, a Helicarrier, The Power of Protection x2, and Phoenix's Psionic Bond resource, it's not hard to pull together the resources to play multiple cards per turn and satisfy Black Widow’s requirement or What Doesn't Kill Me’s requirement. Add The X-Jet (one copy of Ever Vigilant is the easiest choice for a card to drop to get back down to 40) if the other characters in the game aren't putting one out to share.