Summarize Hamlet's comments about the first players performance in scene two lines 558-588 of William Shakespeare's play.

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In Act II, Scene II, of William Shakespeare’s Hamlet, the title character is both depressed and determined to delude others regarding the state of his mental health. In short, he is pretending to be delusional so that others, particularly Polonius and, through his spies, Rosencrantz and Guildenstern, King Claudius.  This scene includes one of Shakespeare’s more clever narrative developments, as Hamlet, seemingly excited by the arrival of a traveling theater troupe, specifically requests of the visiting actors that they perform Virgil’s epic Aeneid.  In that story, Pyrrhus, the son of Achilles, successfully avenges his father’s death at the hands (or, more precisely, at the tip of the arrow) of Paris, whose actions precipitated the entire bloody affair when he abducted Helen.  Surreptitiously entering Troy in the infamous “Trojan Horse” of mythological fame, Pyyrhus kills King Priam, Paris’ and Hector’s father.  It’s all rather complicated, but suffice to say, Shakespeare’s point is that Hamlet is cleverly arranging a production in which his mother and uncle, King Claudius, will sit witness to a production designed to replicate the latter’s treachery.  Hamlet first instructs the “First Player,” one of the actors, to recite the relevant passage from the Aeneid.  Hamlet then asks the actors to perform the following evening The Murder of Gonzago, the plot of which mirrors the events surrounding the murder of Hamlet’s father. 

Following the discussion with the actors, in the presence of the apparently oblivious Polonius, Hamlet excuses the troupe and Rosencrantz so that he may contemplate his next steps, but not before chastising himself for what he perceives as his lack of courage and failure to date to avenge his father’s death as done by Pyrrhus, who avenged his father, Achilles’ death during the sack of Troy.  When Hamlet compares himself unfavorably to the deeply-felt emotions of the professional actor, he states:

     O, what a rogue and peasant slave am I! 
   Is it not monstrous that this player here, 
   But in a fiction, in a dream of passion,  

     Could force his soul so to his own conceit 
   That from her working all his visage wann'd, 
   Tears in his eyes, distraction in his aspect, 
   A broken voice, and his whole function suiting 
   With forms to his conceit? and all for nothing! 

Hamlet is criticizing himself for his inability to capture the passion required to carry out the violent, desperate acts that need to occur.  Hamlet’s soliloquy reflects his anguish regarding what he perceives to be his shortcomings in his inability to demonstrate the revolve and violence necessary to exact justice.  “Am I a coward?” he asks himself.   “I am pigeon-livered and lack gall,” he berates himself.  Hamlet’s soliloquy is a classic literary example of existential self-flagellation.  Hamlet is more than a little impressed with the actors’ performance, and seeks in that performance as model for the emotional intensity he feels he needs to bring to the game.