The last island is one long chain. Give the scientist five creatures for the Fish Bucket, use it to catch and kill the Bowhead Whale, carry the body up the volcano and throw it into the crater, kill the Mutated Bowhead Whale that comes out, and hand the Whale Fin to the scientist. The military boat then takes you home and the credits roll.
Gear: the Assault Rifle kit
The military supplies next to the landing sell everything, including the Assault Rifle ($20,000). It is the weapon for both whales. Max its bullet damage (this island sells every tier), add the Extended Mag ($5,400), and buy every extra inventory slot so you can carry the whale body and food at the same time.
If you are short of money, the Scientific Lure ($500) catches the best regular fish in the game. The Oarfish sells for $1,450 raw and the Superdwarf Fish for $2,200, and you can throw a catch into a lava stream to cook it for the same 1.5x as the grill. With kill-score trick shots on top, a single Oarfish can be worth well over $10,000.
Five creatures for the Fish Bucket
The scientist in the yellow hazard suit and face mask asks for five creatures of any kind. The quickest way: throw a lit Dynamite stick into the water and pick up the fish it kills. Throw five at her with Q, and when the counter reads 5/5 press E to take the Fish Bucket.

Catch more fish than the five she needs. Drop the extras on the ground near where you will fight, and some near the lava fields higher up. During both whale fights you can pick them up and eat them in one motion without opening the inventory.
Fight one: the Bowhead Whale
Fit the Fish Bucket on the Fishing Rod and cast from the shore near the camp, then take a few steps back as it bites. If you stay at the waterline, the whale lands its opening body slam right on top of you.

The Bowhead Whale has 20,000 health on Normal and was nerfed in patch 1.0.4. Its pattern is simple. While it is on the ground, walk in close and stay underneath it, firing; it cannot hit you there. When it launches itself high into the air, sprint away without looking back, then return once it has slammed down.
Carry the body into the crater
Do not sell or eat the dead whale; its $8,000 value is a trap. Pick the body up, which puts it in your inventory, and drop the Fishing Rod if you need the slot.
Climb to the mouth of the volcano. The path crosses a few wooden bridges and has some light jumping; follow it up the side of the mountain until you are on the rim, on the side where you can see the camp below. Throw the whale into the crater. It erupts, and the mutated whale bursts out about three seconds later.

Fight two: the Mutated Bowhead Whale
Go back down the mountain to open ground. The Mutated Bowhead Whale has 38,000 health on Normal, but it fights like the first whale with one addition: it spits magma that leaves lava pools on the ground. Use the same rule (stay under it while it is down, run when it launches) and keep stepping out of the lava.
At half health it changes in one way. Instead of one jump and one slam, it bounces three times in a row like a pogo stick. When it goes up, run far and count all three landings before you turn back and shoot.

Grab the food you left on the ground whenever your health drops, then switch straight back to the rifle. Keep the fight near the volcano and the camp; dragging it far out into open water can reset the encounter.
Players who own Dynamite can still use it here: since patch 1.0.12 the final boss takes explosive damage even when it lands on its tail. On Hard (added in 1.0.9) it has 25% more health. Two to four players make this the easiest it gets.
The Whale Fin and the way home
The mutated whale drops meat chunks worth $5,000 each and the Whale Fin, a large pale fin with a glowing crack. Only the fin finishes the game.

Give the fin to the scientist in the yellow suit. She hands you the keys to the military boat moored by the camp. Board it and press E on "Get back to the mainland". The screen fades, We are so back and Deadliest catch unlock, and the credits roll.

After the credits you wake up back on the first island with your boat, so you can keep playing for collections and achievements. If you want Handyman, the bare-hands kill on this boss, read its own guide before your final fight.
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