Be logged in on the site; then use the deletion link. According to http://www.picbadges.com/help/?question=39 you can choose between deactivation and deletion. Besides, there are more privacy settings named on this page so perhaps you can take a look.
URLS:
http://www.picbadges.com/
http://www.picbadges.com/my/deactivate/
Please note that AccountKiller.com is not associated with the business listed on this page. AccountKiller provides easy-to-understand instructions and guides on how to cancel charges and relationships from the list of businesses on our site, we have no affiliation with these businesses.