I think this is fine to be targeted on Dragons, as long as the duellist dies the moment there are no enemy creatures to duel. Not -1 each turn, just kill it off right away. In fact, what about having it lose one attack each turn regardless? That way it won't wipe the enemy field clean every single time. For a Golden Dragon, you'd get ten possible duelling attacks, starting at 10 and dropping down to zero gradually. The targeting is random, yes? If so, it could kill off a bunch of skeletons or photons, then by the time it gets around to fighting a fellow Dragon or buffed Pegasus, it would be too weak to get a kill shot.
One thing not mentioned in the original post: does this overwrite old abilities, like Liquid Shadow? I think it should. Otherwise you have the potential for some serious Growth abuse. That also gives it some applications like Liquid Shadow has - by the way, I LOVE cards that can be used both offensively and defensively, and cards that may be a two-edged sword (pun definitely intended).
I have a rapier that looks a bit like the one in the photo, too - is that a proper grip? I know it's a basket hilt, but I was under the impression one's hand would be entirely behind the guard. The hand in the picture has thumb and forefinger wrapped around the guard.