The auxiliary verb here is "essere" because the verb "guardare" here is intransitive i.e. it doesn't take a direct object (you can't "look" someone, rather, you "look at" someone - in this case it is "she looks at herself"). When "essere" is the auxiliary verb, the past participle matches the gender and number of the subject of the verb. In this case the subject (i.e. the one who is looking) is "she", so "guardato" becomes "guardata". I hope that helps :)
'at herself' would be implied in English, based on the fact that people rarely look at mirrors for any other purpose. It would only be necessary to specify this if there were more context needed, such as if she's sharing a mirror. Any translation that doesn't include that phrase is still valid and shouldn't be marked otherwise.