。
She hid the letter carefully so no one would see it.
Literal
She [topic-は] that letter [object-を] anyone [by-にも] see-passive-not [in a way to-様に] carefully hid.
A multi-piece purpose construction. 誰にも見られないように combines several elements: 誰にも (intensified 'no one' with にも), the passive 見られる ('be seen by'), the negative ない, and ~ように ('so that'). Together they read 'so that it wouldn't be seen by anyone.' 注意深く is the adverbial form of 注意深い ('careful'), describing the manner of hiding. The passive here turns the letter into the patient: it's about whether anyone would witness it, not who specifically might.