When trying to tame the thylacoleo you need a argentavis or something that can pick up a thylacoleo. Definitely bump up as much health on it as you can on it. build a 2x2 base with doors all around it so you can shoot it through the door frames. then grab the thylacoleo with your bird and put him in the little basebuild a 2x2 base with doors all around it so you can shoot it through the door frames.
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.