Hamlet believes man capable of infinite achievement but is himself capable of little action. Show how Hamlet displays this inconsistency
Though the previous post really does get at the heart of it, most of the way that Hamlet shows such hypocrisy is through his speech. In this case, he describes man as having this incredible power of reason such that they have power to be like the gods, yet he himself cannot act on the feelings he has of wanting revenge, etc.
Another great example is in Act IV, scene iv where Hamlet speaks again about the fact that God gave man
...such large discourse,
looking before and after, gave us not
That capability and godlike reason
To fust in us unused.
His idea that man has been given this ability to think things through for a reason, that it is not to be ignored, yet he spends almost the entire play second guessing his own powers of reason and deduction.
I have of late,—but wherefore I know not,—lost all my mirth, forgone all custom of exercises; and indeed, it goes so heavily with my disposition that this goodly frame, the earth, seems to me a sterile promontory; this most excellent canopy, the air, look you, this brave o’erhanging firmament, this majestical roof fretted with golden fire,—why, it appears no other thing to me than a foul and pestilent congregation of vapours. What a piece of work is man! How noble in reason! how infinite in faculties! in form and moving, how express and admirable! in action how like an angel! in apprehension, how like a god! the beauty of the world! the paragon of animals! And yet, to me, what is this quintessence of dust?