"Puzzle boss", alternatively "pahzzl bahs". A puzzle boss is any boss that you absolutely cannot even damage with conventional methods at all and have to exploit some part of the stage to damage it, or to reveal some weak point where you're finally able to damage it. Dave's definition stretches it by including bosses that have some special gimmick to it where you just have to adjust your usual tactics slightly. I think the best example of this is Marauder from nuDoom 2, his only real gimmick is that he puts up a shield that absorbs damage when he's not attacking, but he can't put up the shield while he himself is attacking, so you just have to shoot him while he's attacking. He also said that every boss in the first Metal Gear Solid is a puzzle boss. In fact, according to PigPigGo the first time he used the term was in Metal Gear Revengeance... and he used it to describe Senator Armstrong.
Of course, pretty much most bosses would fall under Dave's definition of a pahzzl bahs, but it seems the only ones he called that are ones he hated to deal with.