。
She must have been studying hard.
Literal
She [topic-は] with-all-one's-might was-studying [must-be-に違いない].
~に違いない ('must be / surely is,' literally 'no different from X') is a marker of strong inferential certainty — the speaker is convinced of something based on evidence, not directly observing it. Attaching it to ~ていた ('was doing') gives 'must have been doing' — a confident inference about past behavior. The construction is a workhorse of mystery, deduction, and gossip: it's how Japanese expresses 'she must have done X' on the basis of clues. In casual speech ~に違いない often softens to ~に違いないよ or even drops to ~だろう.