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.
(..) Everyone is talking about Nicolas Sarkozy. Omnipresent. Media darling. Government spokesman. He never thought twice about declaring his ambition. Cecilia his wife is not happy. She regrets the Ministry. By becoming President, Sarkozy has overcome personal odds. Today is the day. (..)2016 Me Before You