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.
(..) Nottingham is mounting an army. He has every blacksmith in the county making swords and armor. -What's his plan? -I don't know. There's no limit to his ambitions. -Thank you. -Quickly. Go! Do something for me. Take a bath. A bath? (..)1991 Robin Hood: Prince of Thieves