。
She really hates dogs.
Literal
She [topic-は] great [genitive-の] dog-disliker is.
大の~ is an intensifier 'a great / huge X' used with personal traits or fan/hater compounds: 大の犬好き ('a huge dog lover'), 大のサッカーファン ('a huge soccer fan'). Here 大の犬嫌い ('a great dog-disliker') gives 'really hates dogs.' The structure is unique to this 大の~ frame — different from the 大~ noun-prefix (大成功 'big success'), which doesn't take の. 犬嫌い is a compound: 犬 ('dog') + 嫌い ('disliked'); the [noun]+嫌い pattern productively forms 'X-disliker.'