Atticus's heroic quest is to defeat Maycomb's prejudice during the Tom Robinson case and become a proponent of racial equality in his community. Another aspect of Atticus's heroic quest is to protect and defend innocent beings. Atticus is depicted as a morally upright man who defends Tom Robinson in front of the prejudiced jury and community members. Atticus wishes to set a precedent for racial equality and is an advocate for justice. He is aware that Tom Robinson will be found guilty but intends to "jar the jury" by presenting the facts of the case, which prove Tom's innocence. Despite the overwhelming peer pressure and adversity from the majority of his racist neighbors, Atticus follows his own conscience and demonstrates integrity and courage by defending a black man. Through Atticus's heroic quest, he wishes to instill admirable character traits in his children and leads by example. Both Jem and Scout learn the value of tolerance, courage, and the importance of protecting innocent beings by witnessing their father valiantly defend Tom Robinson.

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.