She had been desperately yearning for help.

Literal

She [topic-は] aid [object-を] longed-for.

切望する is a strong verb of yearning — literally 'to cut-wish,' where 切 ('cut') functions adverbially as 'intensely / desperately,' the same morpheme that gives 切に願う ('to fervently wish'). It belongs to a formal, almost literary register; in everyday speech you'd hear 助けを欲しがっていた ('was wanting help') or 助けを必要としていた ('was needing help'). The progressive past ~していた conveys an extended state of longing rather than a one-off act — she'd been stuck in that desperate state for some time.