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.

They prefer cooked meat over raw. Don't waste your precious raw mutton, better cook it, as it tames faster and with higher efficiency.

Shoot it out of its tree, then pick with argie and drop it into a trap/hole. Cook up some mutton beforehand.
Bred a slick navy blue and silver mutation.
Many surfaces are considered 'vertical' for it to climb, including the southern side of Volcano on The Island, from which you can then pounce back into the redwood, which is the biggest leap I've found yet

Theese things are actually marsupials.