I did this pure faction with 2x Doppelganger, copycat, and mirrored Queen.
I refreshed until the second battle was the double bulette room and used Dopplegangers to transform into the bulette.
The third battle I started with Two bulettes and two copycats. Once the devours kicked in it went pretty smoothly.
Not the most efficient use of delve attempts, but a much easier run once the path is set.
Of note, a prior attempt the third battle I only had two bulettes. Having at least one copycat is necessary to generate the brown gems needed.
Mirrored Queen is solely to make the first battle go quicker.