She made tremendous efforts to pass the exam.

Literal

She [topic-は] exam [target-に] pass [in order to-ために], tremendous effort [object-を] did.

~ために is the standard explicit purpose marker — '[verb dict]+ために' = 'in order to X.' Distinct from causal ~ために ('because of'), which attaches to nouns or descriptive clauses. 努力をする (literally 'do effort') is a typical light-verb collocation: many Japanese activity nouns (運動, 勉強, 議論, 努力) are turned into verbs by attaching する, and can be re-verbalized as ~をする for emphasis on the activity itself. たいへんな ('tremendous, considerable') as a な-adjective intensifies the noun.