Looks like a complete description of hypercannons is still way too complicated to explain in the middle of a battle:
“Each gun actually consists of two barrels, Admiral, one mounted inside the other. The mouth of the inner barrel is equivalent in size to a supernova cannon. The outer barrel is three times that width. It appears each gun involves firing two different beams at the same target, although there is no way to ascertain yet if the two beams fire simultaneously.
“Assuming the inner barrel is indeed a supernova, then the outer barrel is unlike any weapon previously deployed by either the Colonies or Imperium. Given the fundamental scaling limits on nova technology, the outer barrel must be something entirely different. The guns are not yet energized but are heavily shielded.”
...
“Based on their fluctuating energy signatures, other characteristics, and my knowledge of relevant research, I believe those are hypercannons — weapons able to fire through hyperspace, specifically the fourth spatial dimension. If I’m correct, then the outer barrel of each gun will be used to create an opening into hyperspace, while the inner barrel would fire a supernova blast into that dimension.”
“Fire at what?”
“Us, Admiral! Although our ship is not technically present in the fourth dimension, we do intersect with it. Just as a point bisects a line, and a line bisects a square, our ship bisects a hypershape surrounding us in 4D space. It is theorized by military researchers that if a powerful enough energy beam, a supernova blast in this case, were fired at that hypershape and crossed our intersection with it, the energy would immediately return to spacetime and strike our hull, having completely bypassed our shields by coming at us from the fourth dimension. We have no defense against that except the hull itself.”
St. James looked at the captain and the colonel, eyes wide. “If they can bypass our shields, the Colonial Fleet would be in grave danger!”
By the process of elimination, I'm going with my original idea of some kind of energy beams that can "push" through a target's shields as if the shields don't exist (like neutrinos through matter), resulting in the beam hitting the hull directly. Seems rather like magic, but I no longer care.