What makes Hamlet “the first true tragedy of character?” (Brode)
Hamlet is a "tragedy of character" because he completely fails any time character is needed. He cannot stand up to the person who murdered his father, he is a coward, he uses women and generally lacks any kind of moral standard.
First, his father tells Hamlet he was murdered by Hamlet's uncle and asks Hamlet to seek revenge. Hamlet fails to act, showing little to no courage or honor. Instead, Hamlet kills Polonius whose worst character trait is being an overbearing father. Hamlet does this by stabbing him through a curtain: not facing your enemy head on shows very little character (and also leads to killing the wrong person!).
Hamlet lacks in moral character when he interacts with Ophelia. Her love for him is undying, but he uses her for his own ambitions and has no regard for her feelings or well being. Hamlet's treatment of Ophelia eventually leads to her death. Hamlet also treats his own mother terribly. His father asks him to spare his mother; Hamlet gets so angry, he disobeys his father and lashes out at his mother. He lacks the character to control his anger.
Hamlet is truly a tragedy of character. He has opportunity after opportunity to do the right thing: to honor his father and mother, to treat his girlfriend with respect and to face his enemy. Never does Hamlet take any of these chances, instead, he dies a tragic disgrace.