The game is very nice but you have major medal and highscore issues...
I got 4,460 meters and fell down with 300+ coins but got neither medal and my highscore stayed at 665, probably my first try. On Firefox btw. Tried on Chrome later, got 4,880 with same result.
When you get a medal unlocked notification, there is probably about 20% chance of it being saved to your account – and 80% of being locked out, forcing you to reset save, refresh, delete scores or even change computer. I did try several things and the "Reset Save" button in options can do wonders. I didn't get my highscore noted but I did get my medals at long last.
While there isn't a clear formula to make medals work, the best tip I can give is: play normally, get your medal criterias, reset save and play a quick game afterwards (i.e. die on purpose). Removing highscore from NG scoreboard can also help, albeit I wasn't able to get another.