First things first:
You don't need to worry about which badges are and aren't already posted here.
If you don't have it already, download
GYTB and place it on your SD card. Delete the 3 files in SD:/3ds/GYTB/badges, put the SD into your 3DS, then use the Badge Arcade to fill up your badge case (IIRC the max in your badge case is 1,000). Take note of which badges you have in the case. Run GYTB, and it will dump the badges in your case. Take out the SD and put it into your PC, then move (not copy) the images into a folder on your PC. Repeat this process until you have images of all of your badges in the folder on your PC, making sure all 1,000 of your badges are different than the ones you dumped last time. You should have to dump 3 time assuming you have 2001-3000 badges. After you've dumped all of your badges and put the badge images into a folder, compress the folder as a ZIP or RAR file and attach it to a post here.