From Nightingale Wiki

The Bandersnatch are a hostile race of large rat-like creatures. The Bandersnatches live in the dark corners of the Realms, moving horribly between the shadows. The creatures hunt in packs, coordinating and navigating through echolocation. A Realm Walker of sensitive hearing might well pick up their lupine batlike shrieks before an attack begins. [1]

"She runs so fearfully quick. You might as well try to catch a Bandersnatch!"[1]

It is a rare creature indeed that has no parallels in Earthly mythology. Yet the Bandersnatch's giant rat tail, its vestigial wing-forelimbs, the bifurcated mout, the unseeing eyes, the reptilian is far beyond the imaginings of anyone but Hieronymous Bosch.[1]