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.
(..) Well, I do want you to leave, Karl. But I want to leave with you. I mean, you think this town is too small for you? Well, it's too small for a man of my ambition. So, what do you say? Join me? Okay. Okay. Now, first, we gotta get you ready for the city. (..)2003 Big Fish
(..) what was wrong. Most times a person grows up gradually... ...while I found myself in a hurry. My muscles and my bones couldn't keep up with my body's ambition. So I spent the better part of three years confined to my bed... ...with the encyclopedia being my only means of exploration. (..)2003 Big Fish