Since the word strong is put into quotations, it would appear that the denotation of the word applicable to this question is forceful and unhesitant. With this definition, then, there are two characters in Shakespeare's Hamlet who demonstrates no weakness: Laertes and Fortinbras.
As the son of Polonius and brother of Ophelia, Laertes displays bold and rash behavior as, having returned from France, he vows revenge against Hamlet for the murder of his father and conspires with King Claudius to slay Hamlet in his desire for revenge, but not before he questions the strength of Claudius, asking why nothing has yet been done. Than, when the king receives a letter from Hamlet, saying that he is returning, Laertes responds,
... But let him come.
It warms the very sickness in my heart
That I shall live and tell him to his teeth,
'Thus diddest thou.'(4.8.57-60)
He wishes to encounter Hamlet so that he may kill him in order to avenge his father's death. And, while he does play into Claudius's trap, Laertes displays his strength of character when, just before Laertes stabs Hamlet with the poisoned rapier, in an aside he says, ''And yet it is almost against my conscience" (5.2.301). But, he does not waiver and tells Hamlet, "Have at you now!" (5.2.306)Then, at the end as Laertes has been wounded, he tells Hamlet that the point of his sword has been poisoned and Hamlet will die; however, he also begs forgiveness of the prince, an act that demonstrates fortitude.
The noble prince who comes to Denmark to avenge his father acts as a foil to the indeterminate Hamlet. His firm determination is an inspiration to Hamlet, who describes Fortinbras as "a delicate and tender prince" (4.4.48) easily incited to fight in the cause of personal or national pride. It is Fortinbras who inspires Hamlet to finally take action himself in avenging his own father.