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.
(..) Authority is not given to you to deny the return of the king, steward. The rule of Gondor is mine and no other's. Come. All has turned to vain ambition. He would even use his grief as a cloak. A thousand years this city has stood. Now, at the whim of a madman, (..)2003 The Lord of the Rings: The Return of the King