the climax of Hamlet isn't even (exactly) the duel; I'd say it is the moment when Hamlet forces the poison down Claudius' throat. Or you might argue that it's the actual moment of Claudius' death. I think it's Hamlet finally taking the action of killing him, because that's what his angst has been about all through the play.
It definitely isn't the killing of Polonius -- which is a fascinating, brilliant moment, and which happens, by the way, almost exactly halfway through the play. That's a major turning point which sets in motion all the action of the second half of the play: Hamlet's exile to England, his offstage adventures with the pirates and his return; Ophelia's madness and suicide; Laertes' return and his eagerness to kill Hamlet. But -- again, as in bed -- a great turning point halfway through doth not a climax make. :-)