Ok I did some more testing and the dragon must have really low magic defense since sleep works surprisingly consistently on it. The real bottleneck is your ability to do damage to it quickly, which is solved by Gomez at level 12 with Water II (Carol at level 12 with Ice II also helps).
On another note I gave the bonus game a shot. It seemed doable at first, but I'm not convinced the first dungeon and boss fight is possible without grinding well past where I gave up (at level 12) given that sleep seems to be ineffective there. I did manage to reach the second town too, but it didn't really help since there isn't much gear Helen can equip anyways.
