。
She grew up to be as beautiful as her mother.
Literal
She [topic-は] grew-up [and-て] mother [like-のように] beautiful became.
母のように means 'like her mother' — の connects the noun 母 to the simile marker ように. 美しくなった uses the i-adjective change pattern: 美しい → 美しく + なる = 'become beautiful.' The sentence follows the common narrative arc of a child growing to match a parent's qualities.