How to Complete Not Getting Hit Challenge
For no-hit I went with Michi and an active skill loadout.
Buckler, Seal of Purity, War Drums, Emerald Ring, with something really cheeky like walking cane (if you have it, trigger it before using your active) and Sacred Effigy.
After a point nothing entered my screen. Her movement speed and boss damage bonus are excellent for this challenge.
Quick Tip: If you’ve been damaged, the challenge will no longer show up in the list of available challenges in the pause menu. This is an easy way to check if you still can complete it in the current run.