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.
(..) Have you forgotten what happened to Dale? Have you forgotten those... ...who died in the firestorm?! And for what purpose? The blind ambition of a Mountain King... ...so riven by greed, he could not... ...see beyond his own desire! Now, now! We must not, any of us... ...be too quick to lay blame. (..)2013 The Hobbit: The Desolation of Smaug