Atticus shows many examples of true courage in To Kill a Mockingbird. Even before the trial begins, he shows courage by being willing to take the case; as a single parent to Scout and Jem, he could have said he didn't want to take this case and no one would have blamed him.
When Tom Robinson is moved to the jail the night before the trial begins, Atticus shows courage by facing a lynch mob that comes to the trial. He knows what he will encounter, but he doesn't even take a gun--just a newspaper and a lightbulb, symbolizing the "light of reason" as opposed to the ignorance of lynching and violence.
Atticus also prepares an actual defense for Robinson. Many believed he would just go through the motions of a criminal trial, but he demonstrates to the jury and the spectators that Tom Robinson could not have committed the crime he is accused of. The person who committed the crime leads with his left, and Tom Robinson's left arm was not usable, having been injured in a cotton gin. Atticus further elicits evidence that suggests Bob Ewell was the one who hit Mayella, arousing the wrath of Ewell, who later goes after Scout and Jem. Atticus doesn't flinch from Ewell's threats, nor does he flinch from the attitudes and gossip of the community--those, including his sister Alexandra, who believe he shouldn't do as much as he is doing to show the truth about the alleged crime.