The easiest way to get this achievement for not using a medkit is on level 1-1 on Easy difficulty. I have spoken to many people on this and it seems there is a trick to this achievement instead of a bug. The achievement description states not using a medkit, but the game gets confused when you break or pickup any object. After doing this at least 3 times with no luck, I tried something new.
Focus primarily on your shield for this one. Block and reflect all laser shots at you back at the enemy to get your kills. I do not suggest using your melee attacks at all unless there is only 1 mob on the screen. Take your time and learn where mobs spawn so you dont run too far forward and get caught with mobs on both sides of you. Move forward slowly, spawn the next set of mobs and once one shoots at you, use your shield to deflect it back and kill the enemy. Take a few steps backwards and try to always keep 8 feet between you and the enemy. As long as they are that far away, they will typically just take another step or 2 closer then fire again. Once they get closer then 8 feet from you, they will sometimes just keep walking up to melee range and attack that way. This makes timing the shots and avoiding damage much more difficult (Yes I know this achievement is for not using a medkit and not the dont take damage, but this strategy must be used if you want them both). The reason you shouldnt attack unless necessary is the game seems to see any broken object or loot as a pickup and a medkit is a pickup. The only thing you can actually loot and not break this achievement is the gems that drop off mobs you have killed. Do NOT break orange crates for the level points, do NOT break the blue boxes for ammo and especially do NOT break the green barrels for a medkit. This also means NEVER fire your weapon since bullets travel off screen, its too easy to hit an object and break open points, ammo or medkit without meaning to.
This achievement is brutally tough to do at the beginning of the game, but it is possible. I personally finished the game on Easy and had every upgrade except Shield Level 3 before going back and attempting this which made is a whole lot easier. I tried to do this and "Untouchable" at the same time, but last group of mobs hit me with a blaster shot and I only got this one for not using medkit. It only popped for me when I did NOT shoot anything, did NOT break anything and did not resupply ammo.
Extremely difficult game, broken chievos, glitched chievos and bad programming made this one of the most frustrating games I have played. I hope this info helps those of you who stuck it out to try to finish what they could.