Carchar's taming process is very simple, you can take some cryopods with Rex puppies ( I use Lvl. 400+, one is enough to fill the entire green bar in a high Carchar lvl) and use Fire Wyvern to kill him close to Carchar, and then carry it by hand. That done, after Carchar sniffs amd eats the body, just mount and go out killing the animals aroud you. It is important to observe the timer in the upper right corner, similar to affectivity icon, because at the end of it you will be dusmounted and you will have to repeat the process, providing another body and, again, riding Carchar through the map. It is feasible to use Desmodus's potion to speed up taming.