There are two parts to your question:
1. You can create a badge for completing a mission by adding the image to the mission Trophy
2. In order for user to complete the mission, you can either add a corresponding action to the missions and all users completing the mission will get the badge. I think details on meta data to be used to define the specific group or people was posted earlier in this group. You can check Jive Advanced Gamification Module: Admin Documentation Or you might want to create a 'fake action', so that it won't be completed automatically, associate it with the mission and complete this mission manually as an admin for the users you would like to reward. (Might not scale if you have dozens of hundreds of users).