。
She's just as beautiful as her older sister.
Literal
She [topic-は] older-sister [comparison-と] same-way [as-に] beautiful.
~と同じように ('in the same way as') is a near-twin of ~と同様に — both express equal comparison. ~ように uses the more general 様 ('appearance, manner, way'), while 同様 packages '同じ-様' into one compact noun. Functionally they're interchangeable, with 同様に reading slightly more formal and 同じように reading slightly more conversational. 美しい sits as the predicate i-adjective.