Chairman is pretty rough.
If you want to go easy mode, just bring Legacy. With both copies of Next Evolution, Legacy Ring, and Lead from the Front, your entire team can become immune to every instance of damage their entire deck can throw out. They only deal Melee and Projectile damage, so with Legacy immune to both and redirecting all of it to himself, everyone else is free to demolish on them with impunity.
For bonus cheese, bring Visionary. A first-turn Brain Burn will put all of his Thugs back under his deck, neutering his Underbosses. She’ll take some damage, but it’s worth it; especially if you use Heroic Interception first to protect her.
Slightly less cheesy methods involve stalling out his deck, timing things so you fill up his trash (and flip him) JUST before he runs out of cards, so on his next turn he A.) Flips, B.) Shuffles his trash into his deck to play a card, C.) Summons an Underboss, and D.) Fails to summon a Thug since his trash is now empty.
It’s good to bring heroes with damage reduction, like Wraith, Unity (Stealth Bot), Naturalist, and Omnitron-X, as well as heavy hitters like Chrono-Ranger, K.N.Y.F.E., and Ra.
Another great strategy is to bring Haka to stuff all of his Thugs (and all but 1-3 of the Underbosses, depending on whether or not you are playing on Advanced mode) in his pants with Savage Mana. Or, even better, play on the Final Wasteland and let the environment remove them from the game entirely! (Just make sure you don’t accidentally remove too many Underbosses and make it so he can’t ever flip. Or do try that once; the video game has a unique game over screen for it!)
Another strategy (not limited to this villain) is to bring Mr. Fixer and Absolute Zero. With Crowbars and Grease Monkey Fist, Fixer can hit one target (preferably Operative) for like 4, and then hit AZ for~7 fire damage. Then AZ can do 7 Cold damage to something, or heal it back. Then, on his turn, use a one-shot for some more damage, and finish it up with Coolant Blast for a massive attack.
Hope that helps! Also I hope I didn’t get ninja’d too hard; I can’t post very reliably, since I’m at work.