Easy and Fast Tame Guide:

1 - Do a trap near RedWood(not on) - 6 Stone Foundations and 10 Stone Door Frames;

2 - Find a good level Thyla(don't find him? he finds you! Just joking wait some time, you can kill the low levels);

3 - Go up and grab him with any flyer who can grab him (I use Argi but you can use another one - see it on "More" on dododex).

4 - Go up to other thylas don't catch you and drop him on your trap;

5 - Spam him with tranq arrows or dards (joking again, if you are using tranq arrows wait 5 seconds until each shot when you see that he os in torpor run just wait 3 seconds);

6 And The Most Important - Feed him death berries (IM JOKING cooked prime or cooked mutton is pretty good but cooked normal one works well too, don't forget narcotics.

Now just killl everithing with him.

Hope this help I think its the easest way to Tame it.

Have a Nice day survivors!