This is a relatively easy achievement that I unlocked on mission 2. Now there may be shorter missions after 2 up until 8 that will get you this quicker, but that doesn't really matter. Here are 2 tips to get this achievement on any level 2-8 that you wish.
1. Manually save the game frequently which is done in the pause menu 2nd option down.
2. It says no healing not no dying. If you take a significant amount of damage where you would normally want to heal, just let the enemy kill you and reload the last checkpoint.
I was playing on sharpshooter and died numerous times and this achievement popped after I exfilled using no bandages or med packs.
I hope this helps and if there's any way this guide can be improved, please let me know.