You can tame easily using a tapejara. Find a thyla that's still on its tree. Use the tapsjara to latch facing the ground on a tree facing the thyla. Then use the ranged taming weapon of your preference.
I actually tamed one of these on accident. I had built a trap for taming a Trike and when searching for one to agro I got jumped at by a Thyla and freaked out and ran to my base but the beast just jumped right into my trap. After that it was easy to knock him out with my tranqs. I named him Cole btw, he was a great guy. But just like any story about your perfect pet on ark.... you lose them. We were on a metal run and I was taking him because he can jump far. When I saw some metal I got off and started hitting it but suddenly I got attacked by 3 terror birds and Cole jumped right off a cliff to catch one. Normally these guys can survive a fall but after saving me from the terror bird he had fallen into a swamp :( . Instantly he was ambushed by a Kapro and two Sarcos. He fought well and killed the first Sarco but in the end he died. I have a gravestone at my old base which reads “ here lies a great frienship that came about by what seems to have been chance but was the invisible connection between him and his soon to be owner that would spend so much time together and still be protecting his beloved friend to his death.” RIP Cole 😰😥😭
This valiant Thyla who life was so unfair to. I just wish I had more time to tell him how much he meant to me. 😟
Build a stone trap that has 6 foundations or more with doorframes. They can’t climb doorframes so don’t use walls (I’m not sure if they can climb walls in the wild but just in case). Use an argent or something that can pick it up, drop it in the trap, knock it out with whatever you have. Be careful and bring lots of narcotics because there torpor goes down really fast. Congratulations you now have a Bear cat Thyla thing!
These things are a must have and relatively easy to tame. Basically all you have to do is get a tapejara and have someone sitting on the back seat with a bunch of tranqs. It’s easiest to have a nice open space. Then just shoot it and slowly fly away from it until it’s knocked out. Then just feed it a couple of narcotics and prime meat and bam! The best tame you could ever ask for!