Not all community-run tournaments have badges as prizes.
The organizer of the tournament must request a badge and it needs to be approved by tournaments@ppy.sh, if they didn't do that, then no one is going to get one. It's probably best if you ask the organizer whether or not they actually did that and whether or not their request was approved.
I'm not sure how long it normally takes, but if they did all that and the tournament has been done for over three months,
tournaments@ppy.sh would be the place to ask for an update.