She must have worked very diligently.

Literal

She [topic-は] very eagerly worked [must have-にちがいない].

Pairing past-tense 働いた with にちがいない gives 'must have worked' — the inference applies retrospectively. The whole clause 熱心に働いた is wrapped by the certainty marker. にちがいない sits at the strong end of the inference scale; weaker possibilities would use ~かもしれない or ~だろう.