I tried to remember what all I needed to do for this tame, and all I could come up with was 'run into the lava to get rid of his web' or something like that. So I got close enough and started the tame. And he killed me in a few hits. So as I was running back to me body, I decided it might be prudent for me to look up the strategy on Petopia forums to refresh my memory and adapt my approach accordingly.
I turned on my Aspect of the Wild, ate some Haste food, and drank a Haste elixir. Then following the strategy in the Petopia guide, I hit Anthriss with my Concussive Shot and then backed into the lava pool to his right (the one with the large rock protruding). I hit Deterrence and then began the tame. And he beat me the snot outta me and I had the tame! Other than getting beat up so badly, it was an easy and quick tame.