Vilgax's Squid Monsters are pets of Vilgax.
Vilgax first used them against the young Ben Tennyson at an unspecified point in time. He intended to feed Ben to them. At some point after, Vilgax had several of them hidden under the sewers of Bellwood (the moist atmosphere being close to Vilgaxia's), where they lay in hibernation until the present, when the plumber Bill Gacks accidentally triggered a device that set their reawakening into motion.
When they emerged, Psyphon led them to destroy Bellwood. Bill Gacks (wearing an ID Mask to make himself look like Vilgax), led them into a trap, and they were successfully contained.
Their appearance is a giant squid monster that has the skin and teeth of a Lucubra.