I went against the Chairman in Rook City with Visionary, Legacy, and the Argent Adept (in that order) on advanced and conceded defeat. Not because we were losing, quite the contrary. Legacy was able to tank almost too well, with Lead from the Front and and his power that grants him damage immunity of one type. Since the Chairman's deck uses primarily Melee and Projectile, there was very little damage that seeped in, and when it did, Visionary and the Adept were more than capable of taking their own hits. Add to that Legacy's Ring, Inspiring Presence, Danger Sense, and his Inspiring Strike heal-y power, and Legacy was able to take all of the damage away from everyone else. When I dropped out, Visionary had 20 HP, Argent 20, and Legacy down to 16.
Our problem, though, came from damage, clearly enough. On advanced mode, the Operative makes it much more difficult for any of these three to damage the Chairman (though with Legacy on the field in his setup of LFTF and Melee immunity, everyone could attack with reckless abandon) for anything that wouldn't be immediately healed with his little dip in the chemical bath. After the Crooked Cop came out (which left the Chairman with only about five cards in his deck, most of which Visionary knew), the team just didn't feel like waiting them out. The Chairman was unlikely to kill any of them easily, until his Hired Guns came back, but by then, Visionary could probably just wipe them with a Maelstrom or two with the Adepts help.
It was a strange match, to be sure. It was the first time Dr Tremata was able to help out with the environment for more than a couple of turns, though, since Legacy just took the 0 damage to allow Visionary to concentrate on damage or the Chairman's deck control. Maybe I'll try it again, but right now I just see it as two of my favourite characters depending too much on Legacy until they can scramble enough power to eliminate the Chairman, then repeating for the Operative, or vice versa. The best thing that could have happened would have been for Visionary to find Wrest the Mind and her Telekinetic Cacoon, pop it onto a minion that attacks everyone, and murder their bosses with him while the Adept heals said minion and his team.
Unfortunately, as lucky as their draw was for Legacy (and it was amazing, getting fully geared by turn two, thanks to the Adept), Visionary sat on almost all of her damage cards from the first turn and just Enlightened herself for a bit when no one else needed it. An interesting challenge, but I might just stick with whatever comes up on advanced mode instead of challenge runs.