She hurried to the station so as not to miss the train.
Literal
She [topic-は] train [to-に] not-miss [purpose-ように] station [toward-へ] hurried.
~ないように ('so as not to') expresses a negative purpose — she hurried specifically to avoid missing the train. 乗り遅れる (のりおくれる) is a compound verb meaning 'to miss (a ride)' — 乗る ('to ride') + 遅れる ('to be late'). 急いだ (いそいだ, 'hurried') is the main verb.