The anagnorosis in Hamlet actually occurs before the sword fighting scene. The entire play is a study of Hamlet's psychology and his ability or lack thereof to act in furtherance of the ghost's commands for revenge. Hamlet spends the entire play trying to prove that the words of the ghost are true and that his uncle Claudius did in fact kill his own brother, King Hamlet, in order to gain the throne. He is trying to find the right time and right place to fulfill the revenge and kill Claudius, but feels that "all occasions do inform against me." He is very frustrated by all of the circumstances that keep him from it, especially the command of the King to have Hamlet sent to England.
Once Hamlet returns though, it is as if he is a new man. He relates to Horatio that he has come to a realization: "there is a divinity that shapes our ends, rough hew them how we will." This means that God or fate have a strong influence on the events of his life and that all he can do is "shape" his life. He has been trying too hard to control everything -- and it just doesn't work that way. He tells Horatio later that he now understands that he has to be ready mentally and emotionally ready for anything -- it is all he can do. As he says, "if it (death) be now, 'tis not to come; if it be not to come, it will be now... the readiness is all." Considered together, these two quotes are Hamlet's anagnorosis: he recognizes that he can't control anything but his own reactions, but that knowledge frees him to finally take action and fulfill his father's final request.