If your trying to tame it don’t get close and personal try to stay a distance away (use a longneck rifle) and bring protection from other animals they spawn in the same area as carnies, purlovias, as well and near the swamps.
So. Taming a thylacoleo isnt really easy. Today was the first time i have tamed a thylacoleo and i must say, trying to find it is a pain. I used my quetzal and a parasaur called "bait" on turret mode to find him. If you cant use a parasaur try just going around the waters near redwoods and try to spot 1. Note: Better use a quetzal if you have one, dino's cant dmg you while holding them with quetzal. Find a thyla, shoot it with a single arrow and when ut falls go and grab it. Carry it into a cage or tranq it till it falls unconcious. You will need around 40-60 cooked meat depending on lvl (i am on 0.2 difficulty). Around 20-40 tranq arrows and at least 200 narcotics. When it falls asleep put in the food od choice and narcotics and wait for it to wake up. It takes about nearly an hour to tame. I hope this helps.It's torpor falls down really quickly so watch out for that. If you need help ask. My name is WakeyJakey