Hades's Belly is a location in Kid Icarus: Uprising. Even though it is named "Hades's Belly", it is an interdimentional location connected to Hades, but it is a dimension that resides within Hades himself. It is where the ground and boss sections of the Lord of the Underworld chapter take place.
After fighting Hades, he attempts to get rid of Pit quickly, remarking how the angel looks good enough to eat. Pit soon finds himself in the god's stomach, which is full of many platforms, puzzles, and cellular versions of enemies. Noticing that Pit is still alive, Hades attempts to get rid of the angel by attacking himself, before deciding to instead have Pit pass "the old-fashioned way". This dimension is also where Hades's Heart is located, which serves as the chapter boss. While Pit is within Hades's Belly, any communication with anyone other than Hades is cut off.
Though called Hades's Belly, this strange place is an entirely different dimension than Hades. So while it shares a link of sorts with the evil god, it seems that destruction inside the belly barely affects Hades himself.