If you're determined to tame Uvuros and not one of his non-elite spawns, then it's definitely possible, just tricky.
The best buddy to get for taming him would be a
Priest. They have Fear Ward and also Holy Nova which
causes no threat. Meaning they can heal you without interrupting your tame.
Now, as Kalliope mentioned, you'll definitely want to start off with
Scorpid Sting to increase his chance to miss. Have Aspect of the Monkey/Dragonhawk on, and also pop
Deterrence. Make sure you begin at the farthest point you can while still being in range to start taming, just to give you those extra few seconds.
I'd highly recommend picking up a
Haste Potion in order to minimize the time that taming takes. Drink this right before clicking tame and it should be over in no time.
You might have to give it a couple attempts, but I'm sure you'll get him.
