To give these mourning duties to your father; /But you must know,
your father lost a father;/ That father lost, lost his, and the
survivor bound/ in filial obligation for some term to do
obsequious sorrow (I.ii.94-98).
The King tells Hamlet that death is a part of the natural order of things and he should get over it. In his mental state, Hamlet is greatly disturbed by the fact that his mother does not share his sense of pain and loss. Once he learns of the murder, he berates himself for not “stepping up to the plate” and avenging his father’s death. Hamlet wonders, "How stand I then, /That have father killed, a mother stained”(IV.iv.58-59). He is asking himself what kind of a person he is if he can allow his father to be murdered and his mother to be married to his uncle so soon after his father's death.
She married. O, most wicked speed, to post/ with such
dexterity to incestuous sheets!/ It is not, nor it cannot come to
good./ But break my heart, for I must hold my tongue (I.ii.162-165)!
Hamlet feels that the marriage is not good, nor can this marriage between Claudius and Gertrude come to any good. He wants to express his true feelings to his mother but, knowing it will hurt her, he remains silent for the time being. This shows his deep emotional attachment to his mother.
Hamlet is also a brave and daring character. There are many examples of his fearless attitude, but three stand out from all the rest. The first occurs when the ghost visits Hamlet, Horatio and Marcellus. Hamlet is determined to meet the ghost: “If it assume my noble father's person, I'll speak to it, though hell itself should gape And bid me hold my peace” (I.ii.267-269). Hamlet insists upon speaking to the ghost, even though it could be a demon rather than his father's spirit. The second example of his bravery is illuminated when he actually sees the ghost:
HAM. It will not speak. Then I will follow it.
HOR. Do not, my lord!
HAM. Why, what should be the fear (I.iv.69-71)?
Though others fear the ghost, Hamlet does not. Another significant incident that portrays Hamlet's daring character occurs when he arranges for the players to perform a slightly altered version of "The Murder of Gonzago", hoping to learn whether or not the King is guilty of his father's murder. “The play's the thing/Wherein I'll catch the conscience of the King”(II.ii.612-613). The King’s reaction to the play will determine what course Hamlet will follow, whether to continue as he has been or to do what the apparition requested of him.
Hamlet also has a bad temper as the audience can see when the meeting between Hamlet and Ophelia goes sour: “You jig, you amble, and you lisp; you nickname God's creatures and make your wantonness your ignorance. Go to, I'll no more on't! It hath made me mad”(III.i.154-156). He tries to hurt Ophelia with his insults. Another scene where he expresses his anger is immediately after killing Polonius as he shouts at his mother:
Here is your husband, like a mildewed ear
Blasting his wholesome brother. Have you eyes?
Could you on this fair mountain leave to feed,
And batten on this moor? Ha! Have you eyes (III.iv.74-77)?
Hamlet tells Gertrude that her new husband is nothing like King Hamlet and berates her for marrying Claudius.
These are Hamlet's most demonstrative character traits as portrayed in Shakespeare's Hamlet. Each of these character traits is important, but the most significant is his bravery and daring. Without bravery, Hamlet would neither have spoken with the ghost, nor baited the King with "The Mousetrap,” nor set into motion the string of events leading to the dramatic conclusion wherein all the major characters are dead.