So I was doing the Black Palace with a friend and we got to Tim Tim Snakeeye. I died, teleported out, used a potion, and teleported back in. I ran all the back to Tim Tim Snakeeye and ran into the battle just before my friend hit the final blow (before it could come up with my cards). He was defeated, but it didn't register the fact that he was defeated. I kept saying "defeat source of corruption in the black palace" on my quest marker. Every time I ran back to the place that Tim Tim Snakeeye would be it would repeat the sentence he says before the battle.
You have to be in the battle when the boss dies to get the quest. Your friend shouldn't have killed it until you got back. That will happen in any dungeon. Always wait for the other player to have pips on the turn to hit for kill. It's not a glitch, it's just bad timing.