。
She's looking forward to watching a horror movie.
Literal
She [topic-は] horror movie [object-を] watch [nominalizer-の] [object-を] is-looking-forward-to.
楽しみにしている is the progressive of 楽しみにする, the standard set expression for 'looking forward to.' 楽しみ is a noun ('enjoyment, anticipated pleasure'), に turns it adverbial, and する completes the predicate. The nominalizer の packages the verb phrase 見る ('watch') as a noun: '(the) watching.' Two をs in a sentence is sometimes flagged as awkward, but here they belong to different clauses (one inside the relative-style nominalization, one for the main predicate) so it's perfectly natural.