1. Get an ichthy with a saddle
2. Find a megalodon underwater
3. Kite the megalodon to shallow water with your ichthy
4. Tranquilize it from the shore or a rock safely
5. Make sure you don't keep shooting it after it is KO (I learned this the hard way)
6. Name it Bruce
I tamed mine by making it come to the shallows and getting it stuck by swimming in circles and using a club, you can get it early by doing this. I used a new club and when I was done it was at quarter health.
These terrors of the ocean may seem a very strong and a late-game tame, but my first megalodon was tamed when I was less than level 20, all I did was go into the water and lure it to a place shallow enough then knocked it with a club, took very long to knock out but it was worth that time.
Make yourself a longbow with plenty of tranqarrows, then build a big enough cage going from shore into the water with trapdoor and ladder close to the Dino gate, build a small platform to shoot from. Get it to chase you and wait for it to come thru the gate, then close the gates to trap it and fire on it till it K.O
Be cautious while taming. Your megalodon WILL attract other megalodons once tamed, just like ichys. Make a saddle while taming so you can head to base ASAP, or exterminate any nearby wild megalodons. If you kill other nearby sharks, you'll get some prime fish meat to help speed the taming process!
South Haven is a great spot to look for these to tame, especially in the bay in the middle of the island, all you have to do to tame one there is kill all the fish in there besides the megalodon you want (I suggest using a baronyx to kill the other fish with its stun ability) and then tranquilizer the one you want with a crossbow.
1. Reinforce your raft with stone foundations, they won't be able to break them.
2. Make them attack your raft and shoot at them with tranq arrows (Bow and crossbow can both be used but a crossbow will be quicker) when they swim away because they are almost unconscious make sure you hit all the arrows you shoot so they won't escape.
3. Tame them with the food of your choice (high level Megalodons will need some narcotics or bio toxin, you won't need it immediately but be prepared).
4. Have fun with your Megalodon!