。
She pretended to be sick.
Literal
She [topic-は] sick is [like-ような] pretense [object-を] did.
であるようなふりをした adds ような ('as if') to the pretense — she acted as though she were sick. ふりをする ('to pretend') takes a modifying clause before ふり. The formal である before ような gives the pretense a deliberate feel.