How to efficiently tame a carcharo:

1. Pick up a rex, paracer, or yuty with a rhynio (preferably wild)

2. Find a carcharo and drop the rex, yuty or paracer near it (if you're traveling with a rex or yuty, strafe right or left to avoid getting bitten repeatedly or shriek at it, pick it up again and shriek at it again when it starts to attack you)

3. Kill all of the argies or small, fast carnivores nearby (so they can't harvest the dino you're about to kill and feed to the carcharo)

4. Kill the rex, yuty or paracer, and drag its body

5. Walk slowly to the carcharo and have it eat the body (your rhynio may tank a hit once in the process)

6. If the carcharo doesn't have a green hexagon with a dino icon on it, than you didn't feed the carcharo correctly, try again. (this mostly happens when the carcharo is already targeting the corpse before you click "drag body", so get away from it far enough that it doesn't, think of a rex's aggro range.)

7. Place a bed next to your rhynio so you can respawn and get your stuff if you die

8.Mount the carcharo, and prepare to abandon your rhynio for about half an hour, and endure freezing temperatures.

9. If your carcharo spawned on far's peak, travel to the frozen tooth, then to the winter's mouth, and eventually stay between the winter's mouth and the whitesky peak area, while killing everything in your path, and avoiding letting your carcharo get attacked. If your carcharo spawned on any other mountain, just follow the path starting from that mountain.

10. Kill everything you can easily kill (focus on groups of pack mules or dinos that spawn in multiples of 3-4) while eating rare flowers until your carcharo is tamed, or until it kicks you off and its eyes turn yellow. (similarly to when a giga gets rage)

11. If you get forcibly dismounted off of your carcharo and die, respawn back to your rhynio, grab another rex, paracer or yuty, drop it near the carcharo, and travel back to your death location.

If you survive, just run a safe distance from the carcharo and die there, since there's not really much you can do.

12. Grab your items back, place a bed nearby, kill the dino you were carrying with your rhynio, and feed it to the carcharo again.

13. Kill everything you can easily kill again until your carcharo is tamed, or until it forcibly dismounts you again, in which you should repeat the last 2 steps again.

Additional information:

A level 150 giga gives 18.1% and a titano gives 22.8% for a lvl 150 carcharo and even less on multiplayer, just don't.

Spam rare flowers to attract medium size pack animals, which give taming affinity much more faster.

You can't damage your own tames when you are riding on a wild carcharo nor will the carcharo attack them, but if you unclaim and kill them, they will grant taming affinity.

You can't attack when you are out of stamina, so keep that in mind while avoiding getting your carcharo hit.