Risk of Rain 2

The description here is a little misleading. What it should say is, without using healing items or support, complete the third teleporter event.

To clarify, your health regen that happens automatically doesn't void this achievement, since there's no way to prevent that from triggering. What does void this achievement is anything external that heals you. Specifically:
 

• No items that grant healing
• No attacks or skills that cause you to heal
• No healing drones repaired that'll heal you

Assuming you're using the Artifact of Command from the roadmap, the first point is easy enough to do, because you can just purposely pick items that aren't healing items. Ones that improve your existing health regen are okay (such as Cautious Slug, which makes you heal faster outside of combat), as are ones that improve your health (such as Topaz Brooch, Personal Shield Generator, and Bison Steak), but ones that add healing, such as Bustling Fungus, Medkit, Harvester's Scythe, etc., will all void this achievement. To be safe though, just avoid any items that mention healing. 

For the second point, this is in reference to certain playable characters that heal when using certain attacks or skills. For example, REX heals with his primary attack, so playing as him is out of the question. Just use a character with no healing abilities, such as Huntress or Engineer. 

For the last point, to be safe, just don't repair any drones on the run at all. 

Lastly, I'm not sure if this was a bug specific to me or what, but when this achievement unlocked for me, I had played the first stage without healing, activated a Newt Altar, went through the portal to the Bazaar Beyond Time, and when I exited into Stage 2, this achievement unlocked. It's definitely not an achievement bug, because all achievements are triggered by ingame challenges, and the challenge also completed. So, if you want to try that, it only required me to beat the first stage, rather than three.