Possible Clues:

• Addressee of the advice 'To thine own self be true'
• "Hamlet, thou art slain" speaker
• Polonius' son
• 'Hamlet' character who (spoiler alert) kills the shit out of Hamlet
• To whom 'to thine own self be true' is said
• Shakespeare character who says 'I dare damnation'
• Real trouble upset Ophelia's brother
• To whom it was said 'to thine own self be true'
• 'Lear' in production set up with part of 'Hamlet'
• Put up scenery with genuine character from Elsinore