Um, basically, a zero-to-death combo is a combo that starts at 0% damage and ends when the opponent flies into the blast zone. Many characters with high speed, chain grabs, drills, and moves that can be Short Hopped Fast Falled (SHFFL) can do these kind of combos. Characters that have fast falling speeds and are bulky in size are prone to these zero-to-death combos.
DK is the biggest out of the entire cast so far, and I have actually faced him with many characters such as Fox, Link, Sora, CFalcon, Mega Man, Mario, and even Ness. His big shield doesn't seem all that great if you're opponents can grab you out of your shield, and most DK players rarely use his down b because of it's starting lag and cooldown. Many of his moves can be punished hard when they miss, and he can do zippity zat against projectiles.
DK has great aerials though, and most of his combos are devastating, but he has trouble approaching, and when he's off the ledge, all you can do is hope for good luck. This is what I mean by strong offense and weak defense.