My fighter (with the feat that gives combat maneuvers and a d6 superiority die) had just reached 2nd level before the Half Dragon offered his challenge. Both me and the dragon rolled a lot of misses, but I eventually won out.
My character is a duelist by nature. I accepted the challenge, since it seemed the Half Dragon was a terrible negotiator (wait, you'll give me what I want if I accept the duel? I don't even have to win?). I was expecting to lose, but I was also hoping that his challenge to fight to the "last man standing" would have allowed my comrades to stabilize and heal me when the fight was over. Instead, through sheer luck, I whooped his half dragon ass.
I had the dueling fighting style, with a Rapier. I usually keep my left hand empty but my group insisted that I'm allowed to use a shield and still get the +2 damage, so I decided to take one for that fight. +5/1d8+5 rapier, AC 18 (scale mail, shield, +2 for 16 dex) and 22 hit points.