You are on a timer. You have to kill them faster.
The shard is from their quest, so you have to kill them before they complete the quest and draw the shard.
The other effect is from their hero card, which replays all their death rattles from the game.
The point here is that you need to finish them faster if you are playing paladin. They will win if it gets into the later turns and you should just concede instead of wasting your time.
You have to smack them down fast, which is why many paladin decks are carrying smite now,