She finally achieved/realized/fulfilled her 'life's ambition' [=the thing she most wanted to do in her life] when she started her own business.
He has 'ambitions' for an acting career. = He has 'ambitions' to become an actor. = His 'ambition' is to be/become an actor.
With her talent and fierce 'ambition' [=her very strong desire to succeed], she became a very successful actress.
(..) Joey Zasa would never pull something like this without the backing. He's just muscle. He doesn't have the wit for that helicopter attack. He doesn't even have the ambition to wipe out the whole Commission. I say we hit back and take Zasa out! Never let anyone know what you're thinking. (..)1990 The Godfather Part III