1. Login to Success Community
Login to Success Community from https://success.salesforce.com. Once login, click your avatar and select "My Profile".
2. Edit Profile
Click "Edit" button then "Profile".
Scroll down to "Certifications & Badges" section and enable both "Show Salesforce certifications on my profile" and "Show Salesforce Trailhead Badges on my profile". Make sure to enter your account and verify it.
Click "Save Changes" and done. You will need to enter verification code sent your email.
3. Check Your Profile
Navigate back to your profile - https://success.salesforce.com/profile then click "Certification and Badges" - https://success.salesforce.com/ProfileCertificationsAndBadges, you should see your hard earned Trailhead Badges and Salesforce Certifications showing off now.
Every user in Success Community will have unique User Id, which is start with 005, example: 00530000003TTvZAAW. When you click someone profile from Success Community, notice the URL, example: https://success.salesforce.com/_ui/core/userprofile/UserProfilePage?u=00530000003TTvZAAW&tab=sfdc.ProfilePlatformFeed
Get the User Id and paste it to following URL: https://success.salesforce.com/ProfileCertificationsAndBadges?u=00530000003TTvZAAW remember to change the Id to that particular User Id.
This is not convenience to manually copy and paste, ideally there should be a link from the user Chatter Feed to User Profile, so vote for this idea.
Another option is by search that people name from search text box and select People.
Search result as below, click the name then Certifications & Badges" link at left menu.