Get rid of the attitude that the reputation is unfair. Often there is a person or group behind spreading hurtful reputations and even if it's untrue, harboring anger about it only fuels the fire. Instead, put your focus on what you want for your reputation.
Separate from old friends who helped give you the bad reputation. As the old saying goes, birds of a feather flock together, and regardless of how open-minded people want to be it's natural for them to assume you still have bad habits judging by the company you keep.
Fess up to your old reputation and don't hide from it. Hiding from a bad reputation only makes someone look guilty. Be honest and tell people what other people formerly knew you for, but that you changed your behavior or that it was untrue in the first place. They will respect your honesty.
Look for opportunities to reinvent yourself. Choose a college in another state or join extracurricular clubs far removed from what you once were. People who don't know you are more likely to give you a chance.
Watch others whom you admire. Watch how they portray themselves in public and how they treat others. Try to imitate their positive qualities and incorporate them into your own life. Don't try to become them, but take those qualities and give them your own individual spin to lose a bad reputation.