User blog comment:Sefranek/Solo Craw challenge.../@comment-3420061-20120610172356

As Auntarie says, you can do it with Leviathan. Hope you have ammo regen, and are safely parked either in the terrain glitch or up on the cliffs (where occasionally Craw's shockwave attack will knock you. that's how I got there), because there's a lot of trial-and-error sighting-in required. Supposedly you can do so with a twisted-type SMG as well.

Easier to run behind him to get a clear shot. If you're a Siren, phasewalk to the other side of the pillars. Any other class, take out his eye, then get on the far side of the map from him outside of his aggro range, and wait for him to turn on his own.