Maybe different color ducks which might have different kind of attacks (I.e. fire damage, electric damage, slash damage.)
Err... elemental moves are something I want to avoid when it comes to Duck Hunt Dog's moves. I feel they don't suit Duck Hunt Dog because they were never part of the NES game.
I guess we could make the neutral special (the duck move) different...
1) have the duck automatically act like a homing missile where it flies toward the opponent and the hunter from the fourth wall automatically shoots the duck when the duck overlaps with the opponent
2) have the dog throw two ducks that randomly fly around the opponents and the hunter from the fourth wall keeps missing the ducks so we have a bunch of gunfire explosions (you know how fireworks explode in the NES Super Mario Bros.? yeah, like those) surrounding opponents and characters get hurt in those gunfire explosions
We could make the side special (the frisbee move) different...
1) the dog throws the frisbee straight but it does not hit the opponent... instead the hunter from the fourth wall keeps missing the frisbee so we have a line of gunfire explosions trailing behind the frisbee and characters get hurt in those gunfire explosions
2) the dog throws the frisbee straight like a regular missile and the hunter from the fourth wall automatically shoots the frisbee when the frisbee overlaps with the opponent