I've seen this question posed a couple of different ways now and after reading the novel myself over a hundred times, I see your struggle... Scout doesn't really win any fight for justice unless you think about this figuratively.
Scout represents the author, who wrote in an effort to possibly affect change for the positive in the civil rights movement. Being a white woman, Harper Lee (personified through Scout) wrote a scantily challenging storyline to make people see racism through the eyes of children. It is almost allegorical of the actual Scottsboro trials, but Harper Lee has claimed that is not exactly what she modeled her storyline from. This work, which is still so widely read and studied in high schools and colleges is continuing to contribute to the understanding the common man has of racial equality. Lee illustrated the evils we have in our hearts and walk around with daily letting them influence our decisions and judgments, just like the jury.
Children are influenced by many experiences throughout childhood that shape an eventual adult. Scout's will, heart, perceptions, and eventual actions have been shaped through the story's events of watching the inequity of the trial, being asked to fit into an expected model of a woman, and experiencing the reality of Boo Radley's identity.
If you feel this question is looking for a specific event, Scout truly wins a fight that represents justice in breaking up the mob that was ready to harass and maybe lynch Tom that night at the jail in chapter 14 or 15. Tom deserved a fair trial and it was possible he wasn't even going to get a trial if that mob had taken him out beforehand. She at least helps justice earn a place to act, although I think we can all agree, justice was not served.
Good luck, this is a tough question to determine what you mean or what your instructor might specifically be looking for.