I believe the correct answer is a duel between Laertes and Hamlet. Laertes had many reasons to want to kill Hamlet, the most important of which are the facts that Hamlet killed Polonius, Laertes' father, and indirectly led to Ophelia, Laertes' sister, committing suicide. So the excerpt above talks about their future duel in which Hamlet says he would kill Laertes in only three hits.
