。
She did it in her own particular way.
Literal
She [topic-は] that [object-を] her own-unique [genitive-の] method [with-で] did.
独特 (dokutoku) is a な-adjective/noun meaning 'unique, distinctive, characteristic of (someone or something).' 彼女独特の ('her own particular') is the attributive form — distinctive of her, peculiar to her. The で here marks 方法 ('method, way') as the means by which the action was done — instrumental で, the same particle as 鉛筆で書く ('write with a pencil') and ハサミで切る ('cut with scissors'). The whole sentence has a slightly admiring or observational tone — implying that her way is recognizable as hers, with personality.