This reminds me of an episode of Futurama where Leela offers Fry some advice:

Leela: Fry. Remember how we talked about you finishing your stories a sentence earlier?

How about Icicle? He'd need some help, sure, but he doesn't need to roll to hit with Copcicles, and it also blocks the cuckoo's line of fire.

Or...

Ultra Boy with Indomitable
Icons Starter Batman

Leaves you with 18 points.

Wouldn't one Dr. Doom from the FF starter set mop the floor with the Cuckoos? He has the range, a way to counter powers from all the way across the board and Energy Explosion, which can go a long way in hurting a group of people with no damage reducers that all sit adjacent to one another.

Icons U Ra's al Ghul / Coordination
E Cheshire
2x Man-Bat Assassin

Martial Artist keyword, 199 points. Might as well have Cheshire bring her daughter along for an even 200.

Man-Bats carry Cheshire and Ra's forward, using Stealth for cover if possible. If you can pull off a Charge while moving adjacent, even better.

Stop in an L-Formation: Chesh and a Man-Bat should be adjacent to Cuckoos in a manner that ties up as many as possible, with your priority being any Cuckoo already on PC. The other Man-Bat should be adjacent to them but *not* a Cuckoo, and Ra's should be adjacent only to the second Man-Bat. (This way if they get Mind-Control off, they can't turn on Ra's.)

Double-plus good if you can get Cheshire into Hindering. Triple-plus if you can get some terrain to cover Ra's as well.

Cheshire is using Poison. Chesh and the Man-Bats are all calling 11 Attack thanks to Ra's. Ra's can shoot through his own teammates thanks to Coordination.

The Cuckoos have to make a choice: Do their pump their Attack in order to pierce that 18 Defense, or do they pump their Defense to protect against that 11 Attack?

You can get up to three actions per turn with Ra's Leadership. Your opponent only gets two. If he tries to run away or X-Heal, then that's an action he isn't using to attack.

Don't be afraid to push a Man-Bat to get in faster. They keep their Defense on their second click, and if they actually do get hit then they get Blades.

-J