Iron Crypticle

Any boss in New Game mode will do for this achievement, but unfortunately, each boss has a few variants with slightly different attack patterns. Ideally, you want a boss variant that doesn't shoot out the purple shots around the arena that turn into spikes, but even with those varients this is still manageable. I found the Boulderface boss to be incredibly easy regardless of variant. Just keep your distance, which is easy to do since he just moves in a square pattern around the center of the arena, and just shoot at him, ignoring the boulders. They'll eventually be destroyed and you'll do plenty of damage to finish him off.

With the multiple runs you'll need to do to get better and more experience, this achievement will likely come naturally. If not, by the time you finish NG+ and the Hard mode achievement, you should have plenty of experience with the game to mop this up on a New Game run.

Below is a video of me beating Boulderface without taking damage (and without using a weapon pickup).

https://www.xbox.com/play/media/6BTHKG29LH