Both Uses

acquit
in
Jane Eyre
(Edited)

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

Being acquitted does not mean the court declared the person innocent. It simply means there was not enough evidence to prove guilt according to the law.

The amount of evidence required depends on the type of case. In a criminal case, where someone could go to prison, the prosecution must prove guilt beyond a reasonable doubt—a very high standard. In a civil case, a lawsuit usually about money, the plaintiff only needs to show that the defendant is responsible more likely than not—a much lower standard.

This is why the same person can be found "not guilty" in a criminal trial (their guilt was not proved beyond a reasonable doubt) but still be found guilty in a civil trial for the same actions (because their guilt was more likely than not).
(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.