And finally, the moment we've been waiting for: the duel between Burr and Hamilton. The story is told from Burr's perspective, because we completely understand Hamilton's perspective, but without looking at the duel from Burr's perspective, we can easily misunderstand his intentions as wrong.
The duel between Hamilton and Burr in the musical Hamilton
As he prepares for the duel, we come to learn that Burr is, surprisingly, not confident at all in himself. He knew Hamilton was a soldier who saw things differently than Burr, as expressed when he says "I watched Hamilton examine the terrain/I wish I could tell you what was happening in his brain". Hamilton had good aim, was confident, and is comfortable with his gun. On the other hand, Burr has none of what Hamilton has, but rather, a strong conviction: to not die and let his daughter become an orphan. If we look at it from this perspective, is Burr really wrong for killing Hamilton? After all, he was mostly just intimidated to protect his daughter.
Just as the count goes to 10 and Burr fires his bullet, times seems to slow down while Hamilton is hesitant about his decision. Does he shoot or does he not shoot? For someone who never hesitates to get what he wants, he finally hesitates, because in this time and point, he doesn't know exactly what he wants. Obviously, he wants to leave a legacy, but does he want to be remembered as the man who pursued greatness after he kills Burr, or does he want to be known as someone who died proudly? He envisions all his closed ones on the other side - Laurens, Washington, and Philip. In the end, he decided the best way to leave his legacy would be to shoot into the air and let himself be killed.
"When Alexander aimed at the sky/He may have been the first one to die/But I'm the one who paid for it". While Burr gets to live, that doesn't mean his life will be busy. He lives with regret of killing Hamilton. He worries that he will be remembered as a villain, that history is not exact - people only remember certain parts, and for Burr, it is most likely that his mistakes will be emphasized while his good-doings will be forgotten. He faced harsh consequences to his reputation after the duel, and went on to make more mistakes in his career, ultimately destroying any hope of leaving a good legacy. But perhaps his biggest mistake was not realizing the world was big enough for both Hamilton and him.