I've spent FOREVER in the sea with 1560 health and an enchanted monkey wizard staff. I've done all the tricks, like squeezing and staying at the top while spamming black demons, but the eels always kill me. I've the red and green shark fin, but not the purple. When do I find it!
I believe there is no pre set time after which the purple shark appears. Just keep on trying and if you think you die too early, try improving your stats (attack if you are killed by something killable and health if you die from the Sea Snakes). Also try using Erase magic to remove the Snakes' missiles and Enchanted Armor to take less damage from them.
The erase magic spell and the health potions are really all you need. When i got the the shark bit i stayed in one of the ditches in the ground below. This stops you from moving and(if you are low enough) will prevent sharks from damaging you. Whenever the snake comes and the blue water balls are about to hit you, use the erase magic spell to get rid of the balls. Also keep using the monkey wizard staff and the octopus king crown with jaspers. Those fireballs will kill the sharks if your staff doesn't. Lastly, use the pink enchanted gloves and any kind of armor to keep you alive just in case.