。
She spent her life in pursuit of truth.
Literal
She [topic-は] whole-life [object-を] truth [object-を] seeking [and-て] spent.
Two をs in one sentence — 一生を過ごす ('spend one's life') and 真実を追い求める ('seek truth') — which Japanese normally avoids in a single clause. The collision is smoothed by the て-form 追い求めて acting adverbially ('spending her life [in the manner of] seeking truth'); the two をs aren't competing for the same predicate. 追い求める is itself a compound verb stacking 追う ('chase') + 求める ('seek') — a more vivid and persistent pursuit than either alone. The phrase has a biographical, almost obituary tone.