Whilst I obviously agree that mortality and death are major themes, I'm not convinced that they are the greatest, most interesting or significant in the play.
Personally, I would focus on the interplay between the real and the unreal; the physical and the imaginary; the actual and fantasy. Hamlet constantly ruminates and dwells on the difference between appearances and reality. We can look at his outburst too Gertrude that his grief exceeds mere appearance: he feelings are more than something that merely "Seems" to be grief. We can look at his outburst at Ophelia, complaining that God has given her one face but she paints herself another. We can look at his suspicions that the Ghost may be a counterfeit sent by the devil or a fiction conjured up by his own overwrought brain. We can look at his interview with Gertrude in her chamber, drawing her attention to the pictures and appearance of the men she has married and trying to draw out a reliable reality from them. We can look at his reaction to the actors and the comparison of his unactioned real grief and the actor's counterfeited convincing grief at Hecuba. We can look at the age old unanswerable question of Hamlet's own "antic disposition".
Throughout the play, the theme of the real and unreal overwhelm Hamlet. If we turn to the graveyard scene, the image of Yorick's skull for me is an image of the final only truth at the heart of man: once the acting and attitudes, the dissimulations and deceits, the disguises and make up, the lies and set faces are stripped away, the only honest truth in humanity lies in the stark visceral reality of our bones.