You might try this method. It works on nickel and chrome-plated guitar parts. Attempt at your own peril, however, because I can't guarantee the result on your badges.
Fill a container with a small amount Muriatic Acid and hang your item a few inches above the Muriatic Acid. Cover with a towel so the fumes stay inside the container. Check on it after a few minutes and then every hour or so until it is aged to your liking.
For other metals, you may want to check this website:
Patina Formulas for Brass, Bronze and Copper
Good Luck!
-e.