The key to earning this badge is to check-in first, wait 15 minutes or so, and then write your review.
I thought it was cheating to use Yelp this way because it looks like I visited the establishment twice in one day, but this is how Yelp works best. Check-in first, wait, then write the review.
As far as the most successful wait time… I earned the badge after a dozen or so attempts. There seems to be a randomizing aspect to Yelp’s programming; however, the combo of check-in/review that finally won it for me was spaced within 45 minutes.