。
She's as smart as anyone in the class.
Literal
She [topic-は] class [of-の] anyone [from-にも] not-inferior head [subject-が] is-good.
誰にも劣らず is a fixed comparative frame that takes some unpacking: 誰 ('anyone') + にも ('even to') + 劣らず (the classical negative form 'without being inferior'). The whole expression means 'inferior to no one, as good as anyone.' The classical ~ず for negation ('without doing') still appears in fixed expressions like this, lending a slightly elevated tone. 頭がいい ('smart, intelligent,' literally 'head is good') is another body-part-attribution idiom — Japanese tends to locate intellectual ability in the head and mental clarity in the eyes (頭が冴える, 目が覚める).