Both Uses of

acquit
in
Jane Eyre

At that hour most of the others were sewing likewise; but one class still stood round Miss Scatcherd's chair reading, and as all was quiet, the subject of their lessons could be heard, together with the manner in which each girl acquitted herself, and the animadversions or commendations of Miss Scatcherd on the performance.
p. 63.9

acquitted = handled (conducted or behaved)

What charade Colonel Dent and his party played, what word they chose, how they acquitted themselves, I no longer remember; but I still see the consultation which followed each scene: I see Mr. Rochester turn to Miss Ingram, and Miss Ingram to him; I see her incline her head towards him, till the jetty curls almost touch his shoulder and wave against his cheek; I hear their mutual whisperings; I recall their interchanged glances; and something even of the feeling roused by the spectacle…
p. 215.2 *

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)
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.