Antigone is one of the bravest characters in all of Greek literature. She shows this in several ways.
First, we need to know a little of the context of what is taking place. Creon, the leader of Thebes, expressly forbids anyone to bury the body of Polynices, who just died in a battle to take over Thebes. Creon wants his body to rot and be eaten by animals as a punishment. I might add that this is one of the worst things that can be done in this society.
Second, within this context, Antigone decides to defy Creon and bury her brother, Polynices. She will risk her life. In the process, she gets caught, but she will not be deterred. This shows great courage. She is about to die on account of her actions, but even then she will not be deterred to follow what is right. Here is quote on her resolve:
"I didn't say yes. I can say no to anything I say vile, and I don't have to count the cost. But because you said yes, all that you can do, for all your crown and your trappings, and your guards—all that your can do is to have me killed."
We can see her courage even more when we look at the other characters. No one has the courage to do the right thing, that is, bury the body of Polynices.