There are many places where Atticus shows courage.
First, it is important to start with Atticus' definition of courage. He defines courage when he talks with Jem. In fact, he wanted Jem to spend time with Dubose to see what true courage is-the ability to fight even when you know that you will lose. He says:
I wanted you to see what real courage is, instead of getting the idea that courage is a man with a gun in his hand. It’s when you know you’re licked before you begin but you begin anyway and you see it through no matter what.
Second, Atticus lives up to his definition of courage, when he says that he will probably lose the case defending Tom Robison. Atticus knows that the odds are against him, but he will still try his best, because it is the right thing to do. Here is his dialogue with Scout:
“Atticus, are we going to win it?"
“Then why - “Simply because we were licked a hundred years before we started is no reason for us not to try to win,” Atticus said.
Finally, Atticus shows courage when he stands up the mob. Moreover, he says that the mob basically were good people who had blindspots. From these words we not only see courage but also charity. Here is what Atticus says to Jem over dinner:
Atticus placed his fork beside his knife and pushed his plate aside. “Mr. Cunningham’s basically a good man,” he said, “he just has his blind spots along with the rest of us."
Jem spoke. “Don’t call that a blind spot. He’da killed you last night when he first went there.
Based on these quotes, Atticus was the bravest man in the book.