。
She must have been beautiful when she was young.
Literal
She [topic-は] young days [contrast-は] beauty was [must be-に違いない].
美人だった (was a beauty/beautiful woman) uses the noun 美人 (beautiful person) rather than the adjective 美しい. The は after 若い頃 adds contrastive emphasis — she was beautiful in her youth, implying the present may be different. に違いない (must have been) expresses strong inference about the past based on the speaker's reasoning, distinct from かもしれない (might have been) which leaves more room for doubt.