Demon Spawners are enemies that spawn in the Demon Halls and look like red balls. They are connected to Yog-Dzewa—the final boss in the game. If the Badder Bosses challenge is disabled (which can be enabled by clicking the gear icon in the hero selection screen), each Demon Spawner will give Yog a 25% chance of spawning a Ripper Demon instead of a God's Larva, but if the challenge is enabled, Yog will also spawn Evil Eyes and Scorpios if Demon Spawners are alive. To get this badge, you need to kill Yog without killing any Demon Spawner.
Each level in the demon halls (levels 20-24) has one. I always go after them at the start of each level; otherwise you'll have to deal with lots of demon rippers.