The redwoods are now basically a no fly zone, I lost a quetz, and a pter to these bastards. They jump out of the tree, rip you off your mount, and then pin you and your mastercraft armor to the ground and murder you.

Easiest way to tame: make a dino pen, pick one up with an argy, put it in the dino pen then follow along with a basic taming process (knock it out, feed it). Make sure you have lots of narcotics on you!
Best thing about them: they can climb up really steep hills and they can potentially do lots of damage and can be fast.
Where to find: most commonly found on trees (they will be hanging upside down, high up on large trees) in the redwood forest areas (mainly on The Center) or I find lots of them in the Ragnorok desert.

Very good tame! They're like pet tigers.

Fly around on an argie while holding a parasaur on turret mode, the parasaur will sense it but make sure the thylacoleo can't reach you by flying high above so it hits the parasaur rather than you.

If your on Ragnarok, I suggest taming them in the desert, in my opinion its alot less dangerous b/c the thylas are on the ground. Make sure to go on a flying mount and watch out for rock golems and other bugs. The thylas are near the bottom of the desert.