In Bearbaiting, make sure you kill both flak guns (and, of course, at least two beam turrets). Command is correct: "The more turrets we disable, the better our chances." If you do well in Bearbaiting, it makes High Noon much easier.
Counterintuitively, it's easier to destroy the flak turrets if you shoot them from the bottom, in their blind spot. (It has to do with the submodel placement.) Four Trebs will knock out one flak turret.
I always play Bearbaiting repeatedly until I get all four beams. Lately, I've been playing it until I get every single objective (the four beams, the two flak guns, the bonus gun, the three turrets on the Demon, and the Demon itself) before advancing to High Noon. I actually haven't played High Noon with less than four beams destroyed in quite a while.