I 'beat' Advanced Ennead here with Legacy, Parse, and Wraith. It's possible, although improbable. And all other characters can deal non-projectile non-melee damage. (Well, Setback can't except to himself, but he can redirect villain damage, which works just as well)
I just did the math for the AZ, AA, Bunker vs Matriarch matchup mentioned above, and it's easy.
Round one:
Horrid Cacophony x2, Impale, Syncophated Onslaught (Bunker & AZ), Flak Cannon [4], Toxic Sludge [5]. Matriarch at 61.
Round two:
Darken the Skies x2, ([3] from first Impale), Impale, Xu's Bell, (onslaught Bunker & AZ, [1]), Grenade Launcher (cannon [4]), Second Toxic Sludge [10]. Matriarch at 43.
Round three:
Carrion Fields x2, ([6] from Impales), Cold Snap, <some ongoing or equipment>, (onslaught Bunker & AZ, [1], Turret Mode [9], Dr. Tremane ([10] from sludge). Matriarch at 17.
Round four: Darken the Skies, Hugin (destroy AA's extra card), [8] from AZ's start of turn, [1] from AA, [9] from Bunker. Matriarch is at -1.
And I didn't even bother to try complicated shenanigans with AA.
Round four is the sweet spot for the Matriarch. If you deal 70 damage to her before round 5, then (as demonstrated) you can basically ignore her deck. Infinitor is probably going to be harder.