。
He steeled his resolve and embarked on the venture of a lifetime.
Literal
He [topic-は] navel [object-を] hardened one-generation-one-era [possessive-の] great-enterprise [to-に] set-out.
臍を固める (ほぞをかためる, 'to harden one's navel') means 'to steel one's resolve, to make up one's mind firmly.' 一世一代 (いっせいちだい, 'once in a lifetime') is a 四字熟語. 大事業 ('great enterprise') is the venture. 乗り出す ('to set out into, to embark on') is a compound verb for launching into something. The sentence is dramatic narrative prose about a momentous decision.