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.
(..) the street is giving me a hand... ...and I'm giving him $. Tha's Henry Jackson? Yes. I's funny what happens in two years. Nine years old, has great ambitions. Listen, about my last visit... Pish-posh, we needn't talk about it. I's water over the dam or under the bridge or wherever you like it. (..)2004 Spider-Man 2