Both Uses of

acquit
in
Henry IV, Part 2

If my tongue cannot entreat you to acquit me, will you command me to use my legs?†
Scene 5.5 *

acquit = officially find "not guilty"

Then take, my Lord of Westmoreland, this schedule, For this contains our general grievances: Each several article herein redress'd, All members of our cause, both here and hence, That are insinew'd to this action, Acquitted by a true substantial form And present execution of our wills To us and to our purposes confined, We come within our awful banks again And knit our powers to the arm of peace.†
Scene 4.1

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.