Skip to the bottom for my suggestion on the simplest way to do it
To play exactly will be difficult using only the Quarriors dice. In dice masters every character has 3 distinct sides and this is only true for a few of the creatures in Quarriors. So you may have to do a second roll (or coin flip) to determine the exact side. Or only use the quarrior dice to draw and then just roll a regular d6 instead.
Similarly for the sidekicks, they only have 1 character face and 5 distinct energy sides. So you can use the assistant dice but will have to further resolve your rolls to decide exactly what face you are on. Or you can use the quiddity dice (the 2 is the sidekick face) and either ignore the energy types or mark up your quiddity dice so that each face is unique.
Or you could use the assistant dice almost as they are. Ignore the energy types, character faces are sidekicks, and make the reroll an energy face (maybe worth 2).
If you are mostly looking to try the game rules then the simplest solution is
-no specific energy
-use quiddity as sidekick dice
-Deathdealer = Human Torch
-Dragon = Colossus
-Ghost = Gambit
-Goblin = Black Widow (Green Goblin stats don't really match at unfortunately)
-Use the values printed on the dice
-I'd set up like Quarriors with a common wilds and 5 dice on each card
I chose those dice because they have the most attack oriented values which I think is better for dice masters. But these dice also match values fairly well
-Defender of the Pale = Mr Fantastic
-Witching Hag = Ghost Rider or Green Goblin
-Warrior = Angel
and Ooze's ? marks seem to fit Mystique nicely.
And for even simpler don't use abilities. Then you don't need to print anything, just look at the cheapest purchasing cost for each character and a regular die to mark it on thequarriors card.