"Ambitious" is a good word to describe someone who has a large ambition or goal. You could also say that someone is "determined" or "driven" if they have a strong desire to achieve something. For example, you could say:
She has a lot of ambition and is always working hard to achieve her goals.
He's a very determined person, with a strong desire to succeed.
She's a very driven individual, always striving to achieve her dreams.
These phrases all convey the idea that someone has a large ambition or is motivated to achieve something.