。
She'll only have the very best.
Literal
She [topic-は] highest-grade [genitive-の] thing [only-しか] does-not-prefer.
The ~しか~ない frame ('only X / nothing but X') always pairs しか with a negative verb, even when the meaning is positive — 最高級のものしか好まない reads naturally as 'only likes the top-quality' even though 好まない is literally 'doesn't prefer.' English collapses this into a single 'only,' but Japanese keeps the structure transparent: 'as for anything other than X, doesn't prefer it.' 好む is a more written/formal verb than 好き — emotional preference in conversation usually goes to が好き. 最高級 ('highest grade') is a Sino-Japanese compound that's productive in luxury and quality contexts: 高級 ('high-class') + 最 ('most') = top-tier.