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He was sick of being constantly slandered by people who envied his talent.
Literal
He [topic-は] always his talent [object-を] envy people [from-から] slander-passive thing [target-に] fed-up [progressive-ていた].
A long sentence built on a relative clause. The clause [常時彼の才能をねたむ] modifies 人々 ('people') — 'people who constantly envy his talent.' Then the passive 中傷される ('be slandered') with から marking the agent ('by people'). The whole nominalized phrase 中傷されること is the target of 'fed up with' (うんざりする). うんざり is a 擬態語 mimetic for the feeling of being thoroughly fed up or weary.