All 4 Uses of

acquit

in

Inheritance, by Christopher Paolini

Ever since Katrina's father, Sloan, had betrayed the villagers of Carvahall and killed Mandel's father, Byrd, Mandel had seemed desperate to prove himself the equal of any man in the village; he had acquitted himself with honor in the last two battles between the Varden and the Empire.
Chpt 13

acquitted = handled (conducted or behaved)

It was as if she wanted something from him, as if she wanted him to prove …. what, he knew not, but he was determined to acquit himself as well as he could.
Chpt 24 *

acquit = handle (conduct or behave)

You acquitted yourself well, Eragon.
Chpt 70

acquitted = handled (conducted or behaved)

Definitions:

(1) (acquit as in: she was acquitted)
to officially find "not guilty" of criminal charges

Note that to be acquitted is not the same as being declared innocent of an offense due to the presumption of innocence in the American judicial system. The court determines if there is sufficient evidence to find someone guilty. Some crimes require a lot of evidence for a conviction, so while there may not be enough evidence to declare someone guilty beyond a shadow of a doubt, there also may not be enough evidence to declare a defendant innocent except through the presumption of innocence.
(2) (acquit as in: she acquitted herself well)
to handle oneself in a specified way -- which is typically in a positive way
(3) (meaning too rare to warrant focus)
Much less commonly and archaically, acquit can have other meanings. It can mean to release from a duty, as when Jane Austen wrote "I cannot acquit him of that duty" in her novel, Pride and Prejudice.

It can also mean to perform or complete an obligation, as when Charles Dickens wrote "I have a business charge to acquit myself of," in his novel, A Tale of Two Cities.