I'm sure Paul will jump in here, but I just spotted this whilst looking for something else. This has been mentioned a couple of times.
It's not spam - I would call it a persistant pop-up.
This is actually intended behaviour, your users need to click the button on the achivement which says, if I remember 'view 'users' achievements.
I know that Paul has mentioned he maybe doing something that will change that behaviour as it seems some aren't so keen.
For now I have changed the text on the pop up button to say 'Click to accept this achievement'
The file you need is - feedback-achievement-unlocked.php
Move that file into your themes folder. I altered the text after php_e as follows:
<p><a class="dpa-notification-cta" href="<?php echo esc_url( $user_profile_url ); ?>"><?php _e( 'Click to accept this achievement', 'dpa' ); ?></a></p>
don't know if that helps at all?