。
She became the talk of the country.
Literal
She [topic-は] that country [in-で] topic [genitive-の] person [as-となった] became.
~となる ('become') is a slightly more formal variant of ~になる, often used in narrative or written contexts. 話題の人 ('person of the moment, person being talked about,' lit. 'the topic person') is a stock journalistic phrase for someone in the news — could be from achievement, scandal, controversy, or sudden fame. その国で uses で in its location-of-action sense: 'in [that country].' The whole sentence reads like the opening line of a profile piece.