Banjo-Tooie

Just to elaborate on SpeedyBlueDude's explanation. There are 4 locations. I tried to list all the possible ways to get to the octopi.

1) When you first go down the big hole in Jolly Roger's Lagoon, take a left at the underwater spaceship (past two of the Blubbuls (otherwise known as the orange jelly things)) in to a green path. Use the methods SBD described to freeze the inky (the octopus).

2) Once you've reached Atlantis, take a left and you'll notice a green passage past the lone Blubbul. To help orient you, this passage is between the Ancient Swimming Baths and the Temple of Fishes. This inky path connects Atlantis with the sunken ship room.

3) Swim in to the hole in the sunken ship and take a right through the blue passage to find the third inky. This passage connects the sunken ship with the lockers cavern. If you went the other way and had already discovered the lockers cavern, you can alternatively find K. Connell's locker and swim up and to the right to find the green passage connecting to the sunken ship room.

4) From the lockers cavern, find S. Hurst's locker and you will find another green passage up and to the right of it. This passage connects to the sea bottom/big fish cavern. Alternatively, you can find this passage by climbing to the top of the seaweed sanctum. Once you're in the big fish cavern, simply swim to the bottom left of the big room (past the teleportation pad) to find the green passage and the forth inky.

Bloop! Achievement is yours :)

To get this, freeze the big octopis (the Octopuses) in Jolly Rogers bay. To freeze them, use the Torpedo transformation (gotten from Humba Wumba) Sonar attack or hit them with a ice egg from regular Banjo and Kazooie.
Edit: I forgot to mention, you don't need to freeze them all at once. As long as you freeze each at least once, you get the achievement.