World War Z

Play offline or in a premade group.
You can not press to heal yourself and you're not allowed to let another player heal you. Unfortunately if someone does start to heal you then you can't do anything to stop them.
I believe dying and then respawning is fine.

One thing that's very important, when the achievement description states that you must 'finish any level', I assumed along with many others that this meant a full location.

No... so, there are 4 locations (or episodes) [New York, Jerusalem, Moscow and Tokyo].
Each of these is then further subdivided by 3 chapters (or levels).
A 'level' is equivalent to a 'chapter' in this context.

So an example of completing this achievement would be finishing 'Episode 1: New York; Chapter 1: Descent' from beginning to end without healing yourself or anyone else healing you.

You do not have to complete 'Descent', 'Tunnel Vision' and 'Hell and High Water' to achieve it.

I did this in the second level of the Jerusalem episode: Dead Sea Stroll on Easy with 3 bots. I had a level 23 Fixer and used a fully maxed out Scout Rifle. Not too difficult--I moved through the level slowly and used my silenced rifle to pick off zombies (including the faked sleepers) from a distance. During the horde attacks, I used a stationary machine gun to thin numbers and the bots did a good job of keeping the zombies off of me. I hung behind them once the defense tools were used up.
Note: I was downed twice (and revived by an NPC )during the last section grabbing car parts for the van but this did not affect the achievement. Got it on my first attempt of going for this specific achievement. Good luck on your attempts!

The way I got this Achievement:
- Join a CO-OP online campaign with randoms or friends
- Make sure there is at least one Medic in the group, preferably level 30
- Make sure the Medic gets all the equipment bags.
- Let the Medic Stim-shot you often, this way you avoid using medkits.

This is extremely easy if you have other experienced players with you, or if you are playing on a low difficulty.

The easiest way is to play online with others that at least understand what's going on with friends you know. Set your difficulty to EASY and try your best to avoid damage by either sticking in the back or as a full group.