。
She is just as beautiful as her older sister.
Literal
She [also-も] older-sister [with-と] similarly beautiful-person.
同様に (どうように, 'in the same way, similarly') sets up a comparison — と同様に is slightly formal, more common in written Japanese than the casual と同じくらい. 美人 (びじん) is a noun meaning 'beautiful person/woman,' not an adjective, so the sentence literally says 'she is a beauty in the same way as her sister.'