The other educator does a great job of providing you with quotes and details from the text that support the claim that Atticus is successful in achieving his goal.

If the goal of Atticus taking on Tom Robinson’s case was to show his children that the right choice is not always the easiest to endure, yet it is still important to choose wisely, then certainly he is successful.

If his goal—which is the goal of every lawyer—is to win in favor of his client, then Atticus is unsuccessful.

Besides receiving a guilty verdict against his client, Atticus is unable to protect Robinson from further pain and suffering, even after he is convicted of a crime he did not commit.

Robinson’s death while incarcerated indicates that Atticus failed. In chapter 24, when Atticus announces that Robinson has been killed, Calpurnia refers to his death as the “last straw.” Atticus replies:

What was one Negro, more or less, among two hundred of ‘em? He wasn’t Tom to them, he was an escaping prisoner

While this quote could certainly be interpreted as a matter-of-fact description of the prison guards’ motives for shooting Robinson, the quote could also be interpreted differently. One could argue that the quote shows how Atticus is always willing to make excuses for the wrong actions of others rather than directly condemning them. Instead of criticizing the prison guards’ use of force in a situation where it wasn’t necessary, Atticus speculates on Robinson’s motive in trying to escape within plain view of the armed guards.

In this way, you could certainly say Atticus fails because he doesn’t change from the beginning to the end of the text, and while he may have impacted his own children, he doesn’t really change Maycomb, either. In the end, Tom Robinson is just another statistic, and Atticus Finch gets to continue his legal practice in his hometown.

Atticus is a success because he raised two mature, responsible, compassionate kids and he got the people of Maycomb to think about race differently.  He is also a failure because he did not get Tom Robinson acquitted.  On balance, Atticus is more of a success because he made progress toward racial justice.

Atticus’s success can be measured only based on what you mean by success.  His biggest challenge in the book is the Tom Robison trial, but since there was no way he could win we cannot really count his loss as a failure.  The fact that the jury deliberated shows his success.

"I don't know, but they did it. They've done it before and they did it tonight and they'll do it again and when they do it - seems that only children weep. Good night." (ch 22)

Atticus also has a victory because Jem is weeping.  Jem clearly was raised with a strong moral conscience.  He has also seen his father do something heroic, even if it was not easy.  The kitchen full of food demonstrates how grateful the black population was to him.

Miss Maudie also reminds Jem and Scout that Atticus accomplished a great feat in getting the jury to deliberate at all.

Atticus Finch won't win, he can't win, but he's the only man in these parts who can keep a jury out so long in a case like that. And I thought to myself, well, we're making a step-it's just a baby-step, but it's a step." (ch 12)

In some ways, Atticus does fail, but he does not fail the people of Maycomb.  He is the town’s moral center.