If you want to tame a thylacoleo, I recommend bringing a quick, but powerful mount such as ceratosaurus, carnotaurus, or even a thyla if you already have one. Before you head to the redwoods though, bring an argentavis in a cryopod. Also, make sure you have strong armor, such as flak, or even chitin could work. Ensure you bring a pike for in case you get pounced in the process of searching for one. Make sure you've built a trap somewhere, preferably near or at your base, and ensure that it is a 2x2 made from wood or stronger. To begin, take your mount over to the redwoods and find a high level thylacoleo. You'll spot them hanging upside-down on the thickest redwoods trees, or on the ground. Once you've found one, pull out your argentavis, pick up the thylacoleo, and fly it over to your trap. Drop the thyla into your trap, and tranquilize it. Then, make sure you have roughly 150-250 narcotics to keep it asleep. Feed it cooked prime meat or extraordinary kibble, which is easily obtainable using a yutyrannus egg farm. After it is tamed, enjoy your new thylacoleo!