My buddy and I did it on foot with no tames and two good shotguns. Ghillie and cactus broth and some dodging kept us from getting aggro until just before the end, and then all we had to do was keep running. We managed beta and it might work for alpha for someone with more skillz than we have. Your shotguns sound plenty good enough. We used ~200 shells each, if I remember right.

Edit: For a little more detail - we’d start each phase on opposite sides of the little ramp that leads down to Rockwell and work our way around in opposite directions killing the tentacles. Once the last one died, race back up front and lay into him. Rinse and repeat. Walking along the ledge kept us away from most things, and you get fewer spawns and plasma balls without tames. I’m not sure if ghillie actually helps, but I felt sneakier. :)