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She is recognized as the country's leading figure skater.
Literal
She [topic-は] within-country [at-で] figure-skating 's foremost-person is [quotative-と] is-recognized.
第一人者 ('the foremost person, the leading figure in a field') is a high-prestige Sino-Japanese compound — literally 'first person' — used in journalism and CVs to mark someone as their field's top authority. 認められている is the passive of 認める ('recognize, acknowledge') in the resulting-state ~ている — 'is in a state of being recognized.' The quotative と packages '彼女は…第一人者だ' as the content of recognition. Japanese figure skating has produced major Olympians like Mao Asada and Yuzuru Hanyu, and 国内 ('within the country') sets the geographic scope.