Scaly Pete is the Final boss of the game.
This battle has 3 main ways of attacking/inflicting damage to your character (shark). I will refer to them as A1-A3
A1. His boat that he has rigged to shoot torpedoes at you.
A2. He has electric field (orbs?)(spheres?) things around the boat that do not to much damage, but it does consistent damage.
A3. He sends reinforcements/Divers/Boats after you
to beat him you just have to be aware of how to counter all three of these, as well as how to find time to attack. So the tips i have are here.
First but foremost. If your health gets low hit that sonar scan your shark has (

) and eat some fish. Going further towards the ocean floor you can find fish and enemies to gobble up and not have to worry as much about Scaly Pete's Torpedos
So to evade A1, hit

to dodge out of the way whenever one is going to strike you. After dodging them they should go just past you, Shortly after they go past you they will tip upwards and sit still. Don't just run from them. Pick them up in your sharks mouth holding the right trigger the entire time, Then hold

to go into the slow motion mode where you get to throw things at targets, and simply just throw them back at the boat, If you hit the electric coils under the boat I recall it doing damage to the boat as well. I strongly recommend using this as the main way to attack Scaly Pete's Ship.
for A2 just don't go into the fields unless you get into a situation you have to just go through them for a sec or are really bloodthirsty, Or just want to ego on Scaly pete.
the most annoying for me was A3. The underwater divers are honestly just a pain in this game. they aren't hard to fight at all when they are alone, But with dodging torpedoes and trying to grab them, they do a bit of damage, Just make sure you check around behind you here and there and make sure one isn't just chunking your health. They are good for gaining some health too.
EDIT:
REALLY GOOD TIP FROM Hedganian (A tip for dodging the torpedoes - if you have the bioelectric set activated and fully upgraded, when you hit evade you send out a stun pulse which will short out the torpedo and have it just sit. The area of effect of the stun pulse gives you a bit more time to dodge than doing it without.
It also damages the main boat, so once you've taken out the electric field orbs, you can get up close and personal with PT552 and just spam bite, evade and tail-whip to wreck the boat in next to no time.)~Hedganian
Just rinse and repeat throwing rockets at the boat. If you want to make it more up close and personal too just throw the torpedoes at the shock fields and just keep biting and thrashing his boat.
Right after the ship goes down It will go into a loading screen than the final cutscene and credits. The achievement Should pop somewhere during that period.
He was relatively easy for me but my buddy was having a hard time figuring out the torpedo throwing and the timing on dodging them. So I would assume if this is the part you are struggling with. Just focusing on getting down the torpedo dodging and throwing counter attack down it should be a lot easier.