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It's wrong to aim only for fame.
Literal
Fame [only-だけ] [object-を] objective [dative-に] do [nominalizer-の] [topic-は] wrong [copula-だ].
目的にする = 'make X an objective.' The だけ ('only') narrows the focus to 'just fame.' A moralistic observation, probably from a character-development or ethical context.