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.
(..) I had a free period this morning, Professor. So I noticed. I would think you would want to fill it with Potions. Or is it no longer your ambition to become an Auror? Well, it was, but I was told to have to get an Outstanding in my O.W.L. So you did, when Professor Snape was teaching Potions. (..)2009 Harry Potter and the Half-Blood Prince