、。
I dislike strong-willed women.
Literal
I [topic-は], strong-willed woman [subject-が] dislike [explanatory-なん] is.
A blunt personal opinion. 気が強い is a fixed idiom literally 'the spirit is strong,' meaning 'strong-willed,' and here it works as a relative-clause modifier: 気が強い女 = 'a woman who is strong-willed.' The particle on 気が強い女 is が rather than を because 嫌だ is a な-adjective of emotion/preference — the same family as 好き, 嫌い, 怖い (when predicative), etc. The なんです ending is the explanatory polite form, framing the statement as the speaker's explanation of their feeling.