This thing has so much Health, when I was taming this turtle, my first slingshot broke and I had to make another one and I must have gone through about 50+ stones until it was knocked out, I called it plastic straw for reasons about pollution and the turtles eating plastic (you already knew that)
When taming or attempting to knockout the sling shot is your best option. You can easily get a knockout without taking damage by shooting while backing away since the carbonemys will begin following you after the first shot.
Just get a few spears, then stab them in the head while slowly walking backwards. If your brave enough, us a club to knock them out. But if you don’t want two-thirds of your health gone, use tranq arrows.
If you want to tame this and you are early in the game use a sling shot and slowly walk backwards while hiting it in the head and then when it run go up to it and club it in the head or if you want to kill it slowly walk backwards while stabbing it in the head with a spear and when feeding in take a long time to tame with just berrys.