A later update to the game added a "Dread Knight" Demon, who although appearing in the character choices with the other five demons, does not count towards this achievement. The original five demons must be used. (h/t xPut Name Herex)
There are five Demons you can play as:
Archvile
Marauder
Mancubus
Pain Elemental
Revenant
Play an entire match (best of 5 rounds) as one Demon, then move to the next. At the end of the match with the 5th Demon used, the achievement will unlock.