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That actor really played the cowboy role better than any other actor.
Literal
Truly that actor [topic-は] other [attributive-の] which actor [than-よりも] skillfully cowboy [attributive-の] role [object-を] handled.
A textbook comparative superlative. 他のどのXよりも ('more than any other X') is the standard way to express 'more than all others / best of all,' achieved by combining 他の ('other'), どの ('which'), and より(も) ('compared to'). 上手に is the adverbial form of the な-adjective 上手 ('skilled'). こなす ('to handle, pull off, perform skillfully') is the precise verb for 'pulling off' a difficult task or role — more specific than 'do' or 'perform.' カウボーイ is a katakana loanword from English.