。
She had been sleeping the whole time.
Literal
She [topic-は] the-whole-time was-sleeping.
寝ていました is the polite past progressive of 寝る ('to sleep / lie down'). Combined with ずっと ('the whole time') it covers an extended sleep — a nap that ran long, a person who slept through an event. Note that 寝る in plain past 寝た can mean either 'went to sleep' (perfective) or 'slept' (with adverbial qualification); the ~ている form locks in the ongoing reading. 眠る is a near-synonym focused more on the state of being asleep than the act of going to bed.