She accepts criticism from anyone except her parents.
Literal
She [topic-は] parents other-than [conditional-なら], anyone [possessive-の] criticism [even-でも] accepts.
以外なら ('if it's other than') creates an exception. 誰の批判でも ('anyone's criticism whatsoever') uses でも to mean 'any/whoever.' The sentence reveals a specific boundary in how she handles criticism.