The Giant Squid makes an appearance in the first level of the black puffle section of Puffle Rescue.
The squid is only a shadow that swims under you, but it gives off bubbles that you can bounce on. Those bubbles guide you to a hidden part of the level that brings you Underwater, which has a hidden Moss Key Pin that allows you to gain access to the room whenever you want. However, once you do this, the Giant Squid will not show up again in the game.
It's hard to find, but in Clam Waters, the Giant Squid will make an appearance. Though it does not play an actual role in the game, you are rewarded the Squid Spotter Stamp for finding it.
In Clam Waters, go down to the area with the Mullet. The screen will shake, if you're lucky. When it appears, you will be able to see its shadow (because the water from where it lives in real life is dark) in the background. It'll sink for a few seconds as the screen shakes and quickly swim away.