The Bull Shark is an animal in Far Cry 3
How To Kill A Bull Shark
You can punch a shark but can't kill it with your bare hands
You can only kill a shark using your gun, your knife or a watercraft of some sort.
Note that your guns don't work while you are Swimming.
Shoot at the sharks from land or atop a boat if you want to kill it quickly and with little fuss.
Using a jetski, Patrol Boat or a RHIB is probably the most efficient way to kill bull sharks, though. As this species of shark is relatively common, you can find plenty of them swimming around in the oceans surrounding Rook Island. Look for the fin popping out of the water or shoot some nearby fish if you're having trouble finding a shark (the fish blood will attract sharks.)
From here, killing the sharks is a simple matter of running them all over in your boat. You can kill literally dozens this way in quick succession.
NOTE: Animal Repellent Syringes are ineffective against sharks.