If Beatrice from Much Ado About Nothing gave advice to Scout from To Kill A Mockingbird, what would it be?

Excellent question! I love how this combines two characters that many people would not equate with the other; thinking about the advice that the older, wiser character of Beatrice would give to a young, inexperienced Scout tells us much about them both.
One piece of advice I think Beatrice would give to Scout would be regarding her role as a woman. Beatrice never sold herself short and never confined herself to the proper boundaries that a woman was expected to stay within in her time period. She was not afraid to say exactly what she was thinking, and she gave as good as she got, especially in her quarrels with Benedick. In the play, Hero embodied what a woman was supposed to be like back then: mild, obedient, and virtuous and more of an ornament than an actual person. Beatrice said what she thought, regardless of her listeners.
I think that she would have given this advice to Scout because, even though hundreds of years separated them, what the world expected a woman to be in the 1930s was not as far off as it should have been by then. Scout was censored by Aunt Alexandria for not wearing a dress all the time and was constantly in trouble for speaking out and lashing out. Scout could have been cowed by this; the fact that she was not shows us what a strong person she is already becoming. However, I feel like Beatrice could have helped her by explaining how to be a strong, independent woman who is not afraid to speak her mind without becoming belligerent or bitter. Beatrice never stops speaking her mind, but she does not ever bring people down with her confidence. She still treats others with dignity and kindness.
I think that this is a lesson that many young women today need to learn: how to have the confidence to speak out about what they really think and feel without being rude or unfeeling to others. Beatrice learned how to do that and became a lovable, relatable character. However, if Beatrice were to condense all that information into one short piece of advice for Scout, I think this is how she would have expressed it:
"Be yourself, Scout. For, in truth, no one else will ever do it quite so well."