This badge is awarded immediately after you open the site's tour page while logged in and scroll to the section about badges.
This badge isn't awarded to users who meet its criteria until after a site finishes its private beta. This is because the criteria for this badge used to be undisclosed and this was to prevent people from figuring the criteria out.
Regular badges (except "Informed" and "Beta")
These badges are awarded by scheduled jobs; there are a number of scheduled tasks at different intervals (every few (e.g. 5) minutes; hourly; daily etc) that do a range of things. Most badges are on the "every few minutes" or "every hour" loop.
Badges that check for number of days (e.g. Refiner, Inquisitive, Epic, etc.) are usually awarded once per day, to ensure that users don't earn the badges if they meet the criteria early in the day but cease to meet them by the time the day is over.
General rule: Wait at least 24 hours. If you haven't gotten it by then, you probably didn't meet the criteria for the badge, or you initially met them but ceased to meet them by the time the job ran. Try checking the list of all badges and their exact criteria.
The tag-based badges are calculated on a daily basis at 03:00 UTC, which is when all the tag scores get updated. At that time, any new badges you may have earned will also be awarded, and any badges for which you no longer meet the criteria will be revoked.
Again, if you do not receive the badge at that time, you probably don't meet the criteria, or ceased to meet them by the time the script ran. Hover over your score to make sure that your stats for the tag match the requirements. Also keep in mind that a tag must have at least 100 questions using it before it even qualifies for tag badges.