Hey I was just cruising the forum and literally signed up so I could give some advice haha. I've done exactly what you want to do before, and assuming the badges are plastic you need to sand them, then spray them plastic adhesion promotor, then plastic primer, THEN paint.
It's a pain but I skipped the promoter the first time I tried and the paint started to peel in a couple months, the adhesion promoter totally fixed that when I redid them. Good luck.