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.
(..) Decades of denial Is simply why I'll be king undisputed Respected, saluted And seen for the wonder I am Yes, my teeth and ambitions are bared Be prepared! Yes, our teeth and ambitions are bared Be prepared! Now you wait here. Your father has a marvelous surprise for you. Ooooh. What is it? (..)1994 The Lion King