What is Atticus' heroic quest in To Kill a Mockingbird?
Atticus "heroic quest" is to defeat prejudice and seek justice.
Atticus is heroic because he acts on his beliefs both publically and privately. At home, he teaches his children to act morally and responsibly; he sets an example by acting this way himself.
What sets Atticus apart is that he stands up for his morals in public as well. He defends Tom Robinson when no one else will against the unjust charges against him; most of Maycomb would be perfectly willing to convict Tom simply because he is black and a white woman has accused him of rape.
All heroes must come to a point in their lives when their mettle is tested. In Atticus' case, it is losing his case to acquit Tom. He is sad, but not defeated. This is what he hopes to accomplish....to teach Scout and Jem to solider on and stick to their morals in the face of injustice.