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.
(..) To be honest, I kinda feel sorry for these people. Needing to feel important in these big houses. I talk like this now. But I'm same as every other girl in town. All with same ambition, but... What? You wanted to be a movie star? I loved acting, in school. Where was school? Nebraska. (..)2016 Café Society