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She gives the impression of not being very interested in anything.
Literal
She [topic-は] anything [in-にも] not-very interest [subject-が] not-have [like-ような] impression [object-を] gives.
A multilayered frame: 何事にも + あまり~ない layers a universal interrogative ('in everything') with あまり ('not very, not particularly'), giving a softened universal negation. The whole clause 何事にもあまり関心がない ('doesn't have much interest in anything') is then turned into a noun-modifying simile via ような: 'an impression like X.' 印象を与える is the standard collocation for 'give an impression.' The sentence reads as a measured observation, common in personality assessments or character sketches.