Although Atticus lost the trial, how do Scout's actions show he succeeded?
Another action of Scout that demonstrates Atticus' success is her experience with and analysis of Mrs. Gates, her third grade teacher. Atticus' actions during the trial demonstrated great care and concern for his client despite color. Although Atticus did not win the verdict of not-guilty for his client, he made a baby step for Maycomb that probably (if this were a true story) contributed to the Civil Rights Movement of the 1960s.
In Scout's assessment of Mrs. Gates, she noticed that Mrs. Gates could easily criticize Hitler for persecuting the Jews, but when it came to Sunday mornings, a day wherein a so-called Christian should be on their best Christian behavior, Mrs. Gates demonstrated great hypocrisy by talking about these terrible Negros that the Macomb society had to live with. Scout struggled with this hypocrisy. This demonstrates Atticus' success because at least one soul was changed that day to understand the err of human prejudice.
There are probably several places in the novel, post-trial, where Scout shows what she has learned over the past year. Certainly, the trial is the main event that culminates everything that Atticus stands for and therefore teaches his children by example.
At the end of the novel, then, the one moment that shows Scout's new sense of understanding (perhaps even wisdom) is when Heck Tate proposes that Bob Ewell "fell on his knife." This is a fabrication of truth, meant to protect Boo Radley from entering any kind of lime-light or gossip circle. Atticus asks Scout, "Can you possibly understand?"
Her answer is also the answer to your question:
Yes sir, I understand...Mr.Tate was right...it'd be sort of like shootin' a mockingbird, wouldn't it?