"Final solution" is an odd phrase to use in relation to the deaths in Hamlet, since, in our most common use of the term, it refers to a premeditated slaughter of many people. There are many dead bodies by the end of this play, but they are not the result of one masterminded slaughter.
The deaths in Hamlet come about it these ways:
- Hamlet kills Polonius having no idea who he is. He only knows that there is an eavesdropper, and he kills him. He asks if it is Claudius that he has killed, but there is no evidence in the text that he believes he is killing Claudius when he commits the murder.
- Ophelia drowns either intentionally at her own hand or by accident. Whether this is suicide, is also is not made clear.
- Claudius first tries to have Hamlet murdered on his way to England, but Hamlet turns the tables and Rosencrantz and Guildenstern are killed instead.
- Claudius and Laertes join forces to murder Hamlet, either by the poisoned tip of Laertes sword or a poisoned drink that Claudius will offer Hamlet.
- Gertrude, by accident, drinks the poison and dies.
- Laertes is stabbed by Hamlet with the envenomed sword-tip.
- Claudius is stabbed with the poisoned sword and made to drink the poison -- both at the hands of Hamlet.
- And Hamlet finally also dies from the wound given him by Laertes.
Many deaths, most of them in the final moments of the play, but not deaths that add up to one masterminded "final solution."