Psychic ward does not protect against Mark of the Void 
It’s “void” or “pure” damage, not “psychic” damage.
I’m surprised that it didn’t affect your Berserkers… Are you sure it’s because they were Berserkers?
The way MoV works is that the final boss will cast it once per turn, if possible each time on a different operative. But he can only cast it on characters that cross the rock outcroppings a little after the Gate, so if only one character is in range, he will keep casting it on him. (Actually, he will even cast it on mind controlled Pandorans )
The MoV afflicts the character who receives it, and any allies within 5 tiles, so the trick is to keep your guys a little apart and keep moving.
The Great Artichoke… I mean, the Big Bad Boss… is very vulnerable up close to Rage Burst.