The correct answer is tragic hero.
Hamlet is the hero of the eponymous play written by William Shakespeare. He is definitely tragic - his father is killed, and he is contemplating either revenge or suicide. In the end, he opts for revenge, murdering his uncle Claudius who is the actual culprit, but ultimately dying himself, having been murdered by Laertes.
In this passage, Nick reflects on what the landscape must have looked like when the Dutch explorers arrived to the continent. He is looking at Gatsby's house, and at this point in the novel, we know that Nick believes that New York, as well as the people he has met, are vile, corrupt and greedy. He contrasts this view with that of the pristine continent on the arrival of the European settlers.
The phrase "fresh, green breast of the New World" presents a view that is "fresh." The land is new, but it is also fresh in the sense that it is not rotten. The land has not yet been "infected" with the corruption of modern times. Therefore, the phrase is intended to represent a time before America had become a land of greed and vice.
