。
She must have been very beautiful when she was young.
Literal
She [topic-は] young days [contrast-は] very beautiful was [must be-にちがいない].
とても (very) intensifies 美しかった (was beautiful). にちがいない is the hiragana spelling of に違いない — both forms are standard in writing. The speaker infers past beauty from present evidence with high confidence. とても adds emphasis to the degree of beauty being inferred, beyond a plain 美しかった assertion.