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.
(..) and new purpose when you were cast out, defeated? I was a king! The rightful king of Asgard, betrayed. Your ambition is little and born of childish need. We look beyond the Earth to the greater worlds the Tesseract will unveil. You don't have the Tesseract yet. (..)2012 The Avengers