。
She became famous as a mystery writer.
Literal
She [topic-は] mystery writer [as-として] famous became.
推理作家 (すいりさっか) means 'mystery/detective fiction writer' — 推理 (reasoning/deduction) + 作家 (writer/author). ~として means 'as' or 'in the capacity of.' 有名になった means 'became famous.' Japanese mystery fiction (推理小説) is a major literary genre with a rich tradition.