How to Fish has 28 achievements to unlock, and the Handyman might seem impossible. The achievement not only requires you to complete the game, but you also have to defeat the final boss, a.k.a. the Mutated Bowhead Whale, with your bare hands.
However, the task isn’t as difficult as you might imagine, but it’s still the toughest boss in the game.
How to defeat the final boss with your hands in How to Fish
First, you’ll have to reach the final island with the volcano. Here, you’ll go up against the Mutated Bowhead Whale. Before version 1.0.5, you could directly go to the Volcano Island from the Lighthouse. That is no longer possible, so you will have to follow the systematic route that I have mentioned in the complete walkthrough.

Once you reach the final island, earn enough money to get the Assault Rifle. I would even advise getting all the upgrades before you think about the boss fight.
Next, catch the Bowhead Whale first. This is a weaker version of the final boss, and you will require its carcass to summon the mutated version. To defeat the ordinary Bowhead Whale, you can use your weapon, and that will not be an issue.

Summon the Mutated Bowhead Whale from the top of the volcano. Go down to the military zone because it’s easier to defeat the boss from the flat terrain. You can also store all your healing items to save yourself after taking damage.
While we have to defeat the final boss with our bare hands, we can still use weapons. You have to be careful and ensure that the final killing blow is not delivered using your guns. It must be done by hand. You are also forbidden from using brass knuckles, so nothing but your bare hands will work.

Bring down as much health as possible with your gun before switching to your bare hands. I advise having maximum health before you try the final killing blow, because you could take damage and die otherwise.

I did this solo, but the task is easier if you’re playing in co-op. If one of your buddies manages to land the killing blow correctly, every member in the lobby gets the achievement.