The Black Catling Gun

Black Cat can attack with no consequential damage, so this deck focuses on setting her up to open fire.

Use Suit-Up to search for Black Cat and Sidearm and send her out there packin' heat. The other copy of Suit-Up can help you search for Inspired to also attach to Black Cat so that she does at least 3 damage per shot while taking no consequential damage from herself or any Retaliate.

Black Panther is also helpful for searching for a Suit-Up or banking a Get Ready or Push Ahead if needed instead. Call for Backup is another backup way of summoning someone straight into play if those others aren't working out.

In testing I am dependably able to get Black Cat out there armed. From that point forward, you have plenty of Get Ready and Command Team cards to repeatedly untap her and keep her shooting multiple times per turn. You also have R&D Facility to buff Black Cat for an especially big turn.

As for Spider-Man, he can focus on using his versatile kit to deal with everything else in the game. He has solid defense, Enhanced Spider-Sense can sidestep so many issues, and Backflip can dodge the biggest hits. All the while Black Cat can take care of doing all the damage for you because her repeated shots help to break off Toughness or anything else that needs multiple attacks. All other included allies are decent thwarters, like Moon Girl and especially Falcon.