Arch Dukes are the really big demons with the flaming swords and shields. There are certain activities in which they can appear, but the easiest way is to get your wanted level to 6 red bars. Once this happens, all of the enemies will disappear and an Arch Duke should spawn. Take his health down to a minimum (I used the Armchair-a-geddon) and then simply run up and hit him with a melee attack by clicking
. You can also upgrade your Stonify Blast power and shoot him in the head while he is frozen for maximum damage.