。
She studies as hard as any student in the class.
Literal
She [topic-は] class [of-の] any student [from-にも] not-inferior with-all-might studies.
A 'no less than anyone' superlative construction using どの ('any, which') as the universal quantifier. どの生徒にも劣らず ('inferior to any student' → 'as much as any student') uses the classical negative ~ず form, the older negative inflection still preserved in fixed expressions and elevated language. 一生懸命 is one of those culturally weighty Japanese words: literally 'staking one's whole life' (一生 + 懸命), it captures the cultural ideal of throwing oneself into a task with single-minded dedication — the same word that anchors the school-and-work ethos of total effort. The original form was 一所懸命 ('staking one's life on a single place [of land]'), referring to feudal samurai defending their territory; the modern form generalized the meaning to any all-out effort.