Arch Dukes will be rather uncommon at first. You will come across one per every Marshalling Ground attempt, as they are the formidable mini-boss that awaits you and conquering the teleport for yourself. However, this will only accrue five kills out of the required twenty-five you need. Your best bet for finishing this off quickly is with a fully upgraded Blast power, Soul element, as it will ravage the duke's health substantially. End-game, I only had to shoot it twice and riddle it with holes from my Diamond Sting to see it fall within a minute of it spawning (and a minute is still a generous amount of time to exaggerate with, trust me there).
If, later on in the game, you are finding that you are getting Genki to appear a bit more often, then just simply kill him or use an Activity to reset your notoriety, rinse and repeat. Genki does have a lot of health, though you won't be too pressed with time if you're going for the trophy that also requires you to invest twenty hours of play time as well.