Catching the Speedy Octopus can be a hassle. Luckily, there is a way to reliably get it (minor map spoilers).
Guide to Catch the Speedy Octopus
The Speedy Octopus
The Speedy Octopus is a creature that can be hard to find, and even harder to catch. It spawns in The Open Sea, and then immediately swims along a set path. By speaking with them, you will be given a piece of armor.
How to Setup the Easy Catch
The Home marker is the Neptune Shrine. The X is where you will start and also set your height. The Checkmark is where you will swim to.
At the X, set your height to the level in the picture. Don’t change your height for the rest of this.
Head diagonally north east to the check mark. Swimming in that direction is what causes the Speedy Octopus to spawn.
You want to stop at the Checkmark, with your shadow in the tile shown.
Wait about 10-15 seconds, and press “A” when you have a face full of calamari.
If you miss the timing, then you can either try to chase them down, or just swim back to the X and try again.
A video of the trick being performed on the end game mount. but its possible on the fish.