。
She must have been beautiful when she was young.
Literal
She [topic-は] young days beautiful was [must be-に違いない].
若い頃 (when young, in one's younger days) is the standard expression for referring to someone's youth period — 頃 means 'around that time' or 'period.' 美しかったに違いない applies the strong certainty marker to a past state: the speaker is quite confident about her past beauty based on what they can see or know now. This kind of inference about the past from present evidence is a natural use of ~に違いない.