In the given sentence the subject and the object of the verb is 'her'.
The reflexive pronoun for singular third person is 'himself','herself' or 'itself' according to the gender of the noun.
In the given sentence the noun is a female. So, the reflexive pronoun used must be 'herself'.
Thus option A is the correct answer. Option C is incorrect.
'His' and 'Her' are personal pronouns. Thus options B and D are incorrect.