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She grew up to be as beautiful a woman as her mother.
Literal
She [topic-は] grew-up [and-て] mother [with-と] same [way-ように] beautiful woman became.
母親と同じように means 'in the same way as her mother' — と marks the comparison standard, 同じ means 'same,' and ように means 'in the manner of.' The sentence tells a generational story: the daughter grew to match her mother's beauty. 美しい女性 ('beautiful woman') serves as the result complement of なった.