Mrs. Dubose shows courage when she overcomes her morphine addiction.
Mrs. Dubose is courageous in a different way that Atticus is when he faces down the rabid dog, or the men who help Miss Maudie rescue her furniture from the fire. Mrs. Dubose demonstrates personal courage, both mental and physical. She is addicted to morphine, but she is determined to die without being dependent on it.
In chapter 11, Atticus wants his children to see what “real courage” is because he does not want them to think 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. You rarely win, but sometimes you do. Mrs. Dubose won, all ninety-eight pounds of her. According to her views, she died beholden to nothing and nobody. She was the bravest person I ever knew.” (ch 11)
Atticus wants his children to grow up with their own personal strength, able to stick to their guns and stand up to others. This is about to become even more important because Atticus will need to do this when he defends Tom Robinson, and his children will need to find and defend their own personal convictions as well.