She's just an ordinary girl who has a big dream and she fights for this dream to become true.

She's just an ordinary girl that has a big dream and she's fighting to fulfill that dream. P.S. If you are looking for people to correct you then you should post in the Notebook section.

Vanessa’s answer is good. It might also help you to know that the most idiomatic way to express this — at least in U.S. English — is to use “come” instead of “ become” For whatever reason, “dream come true” — rather than “become true” — is a set phrase in U.S. English. Examples: “She is a dream come true” = “She is a perfect romantic partner for me.” “Getting this job was a dream come true” = I have always wanted to get this job, and now I have it.