I just got awarded the "Tireless" badge on StackOverflow, and have inspected my answers to check if I qualify for the "Unsung Hero" badge.
I have written a query available here, that clearly says that 12/30 accepted answers have zero score. That's both more than 25% and 10.
Do I have to wait a day after getting the "Tireless" badge before getting the "Unsung Hero" one?