Originally Posted by
Azerate
I'd suggest starting with the 'classic' pet tamers from Kalimdor and EK. I think this achievement was in the game since before Legion or even WOD, so that will be the easiest way to complete.
As for Nameless Mystic and Madam Viciosa - those are Broken Shore pet tamers. In Legion, you were only able to battle the pet trainers when their WQ was up. So you can't just go there and battle them. You have to wait for the WQ to cycle to them. Even if they do count towards this achievement, which I'm not sure of, you can't just go and challenge them like the older ones.