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 Um... Don't bother with the chairs What is it your brother does exactly? He's... The keeper of the Broome covet of state, No ambition... No energy... At yet repeatedly told, That he's indispensable to the British government. Particularly the foreign office. I would like to propose a toast. (..)2011 Sherlock Holmes: A Game of Shadows