One way is to enable the ‘BadgeOS Earned User Achievements’ widget from “Appearance > Widgets”. As users earn badges, they will see them appear in the widget.
Users can also see what badges they have completed on any page that uses the BadgeOS shortcode for displaying achievements. Completed achievements are shown in full color and unearned achievements are greyed out, and a menu lets users filter accordingly.
Another method is to use the free BuddyPress plugin in connection with the free Community Add-on to BadgeOS. This allows all or select badges to appear on user profile pages and activity feeds on your site.