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.
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