You'll need to provide more information. Do you have a Mysql database that you are trying to store the high scores or are you just trying to record high scores for your scenario (Which could be done with greenfoots UserInfo database)

Your question is too broad, please see these guidelines for asking questions. In particular, say what part of this of you are having trouble with (or see the "I don't know where to start!" section for advice if you have no idea).