PUT UP YOUR DUKES
Kill an Arch Duke With a Melee Attack
Saints Row: Gat Out of PUT UP YOUR DUKES
Method 1 (Notoriety)
Arch Dukes serve as reinforcement once your notoriety goes up. So you can simply attack enemies until he appears. You can use your weapons and powers to lower his health, but the killing blow has to be with a melee attack.
Method 2 (Marshalling activities)
You can also find him at the end of the Marshalling activities activities. Once you activated all stones he will appear and you can again lower his health and kill him with your melee attack.