。
Her dream is to live a varied life.
Literal
She [topic-は] change [with-に] rich way-of-living [object-を] doing [subject-が] dream is.
変化に富んだ ('rich in variety') is a set phrase. 生き方 ('way of living') uses the productive ~方 suffix. のが夢である uses the nominalizer の to turn the clause into the subject.