Is there any way to retrieve all the badges earned after I inadvertently clicking the refresh button?

If you have reset your gamification badges, please do not worry, as whenever you unlock the next badge in a specific category the previous ones will re-appear. So for example, if a user had 3 badges with 16 logins, thus, once he reaches 32 logins, all previous 3 badges will be restored and the 4th one would be awarded.

So for each badge category, it is a matter of when the next one would be awarded. You should be able to reset any user's badges as per the steps here How to reset the gamification statistics of a single user.