What are some moments in Hamlet that show us what it means to be a true man?
One such moment occurs in Act 1, scene 1, when Horatio and Barnardo discuss young Fortinbras of Norway. Horatio provides some exposition about old king Hamlet's having won some land from old king Fortinbras. Now, however,
"young Fortinbras, / Of unimproved mettle hot and full, / Hath in the skirts of Norway here and there / Sharked up a list of lawless resolutes [...] / [...] to recover of us, by strong hand / And terms compulsatory, those foresaid lands / So by his father lost" (1.1.107-116).
This son responds quickly and decisively to a perceived loss of honor. He is unafraid to be violent when he feels that the situation calls for it. Compared with the way Hamlet behaves later, when he learns that his father has been wronged, Fortinbras acts more like a loyal son and true man.
Likewise, when Laertes returns from France after his father's murder and hushed-up funeral, his behavior also shows what a true man was supposed to act like. When Gertrude tells him to be calm, he says, "That drop of blood that's calm proclaims me / bastard, / Cries 'cuckold' to my father [...]" (4.5.130-132). In other words, he has—appropriately—rushed home to avenge his father's death. He believes that if he were to be calm, he would not be a good son. A good son, a real man, behaves as Fortinbras did: decisively and definitively, without hesitation or weakness. Again, this is the opposite of how Hamlet behaves.