Got the Easy and Medium badges in 2014, but was only able to reach the 980s for the Hard Badge. Tried it again today, and thanks to (what I assume was a glitch), I entered some black hole/warp thing where I went from 660 to 1000 swapping between a black screen and a straight shot. Wish I had won with talent, but a badge is a badge! :)
Was scrolling through my old badges and saw this was one of the two Impossible Badges I've earned since joining in 2013. Almost five years later (January 27, 2016), I can say that I have absolutely no clue how I earned either badge, as I cannot make it more than 30 seconds without dying.
Finally went through and collected the badges on this classic! I ran into an issue earning the Hard Badge: I had all 21 cards, but Kongregate was only showing 20 out of 21. I was able to resolve it by returning to the Title Screen.
Finally! 161 days after earning the Medium Badge, I finally was able to earn the Impossible Badge! :) Similar tactic to everyone else: I purchased 7 Cantrips, 5 Shields, and an extra heart (that I did not need). Just remember to take it slow. As long as you can plan an escape route after every move, and as long as luck is on your side, you should be fine... eventually!
 "Accelerator"){kind=icon}
 "Streamline"){kind=icon}
 "Snowman Attack"){kind=icon}
 "Refraction"){kind=icon}
 "Pawnbarian"){kind=icon}
 "Epic Boss Fighter 2"){kind=icon}