Kill enemies to fill your notoriety bar until it reaches a full circle of six red bars. When the Arch Duke appears, finish him with a melee attack. Consider doing this during a marshaling ground target activity. Activate the two stones to spawn one. The difference between an Arch Duke brought in this way and one that is triggered by earning a high enough alert level is that you can see this one's health bar. Whittle his health down, then swap to your fists to finish him off. Use Coldfire Aura and the freezing ability from it, in combination with Uriel's sword. At least six swings will be needed to kill an Archduke. If you have full duration, it requires well under the duration of one casting to hit your target six times.