Despite previously claiming that there is no way to delete the perma-save in Pac-Man & Galaga Dimensions without "corrupting" the game entirely, Namco Bandai has admitted that there is a secret way of wiping data safely.
Holding down "ABXYLR" when the game boots allows you to quickly reset your save data, contrary to what the publisher originally stated.
The "single save" was copied from Resident Evil: The Mercenaries 3D and seemed intended to combat used games by rendering the cartridge worthless to a second player. It's a controversial idea that many gamers aren't pleased with.
On the one side, it's great that there is a way to restore the cartridge. On another, Namco was either incompetent or outright lying before now, with no indicator as to which.
Pac-Man & Galaga 3DS: You CAN delete saves [Official Nintendo Magazine]