[Achievement] I am invincible

this achievement is doable on any difficulty including "Tourist" (the one I did it on) the biggest issue with difficulty is that for the first 5.25 levels of the game you are having to either use a knife, or rocket launcher, and most of the time you are using the rocket launcher for efficiency, and doing so at zero range.

so to avoid splash damage from your own rockets I would suggest any difficulty below "Normal"
where ammo is a major limiter on any of the standard difficulties. rocket launcher, cannon, and laser are going to be your best choises at any given moment infinite ammo is almost mandatory (unless you realy think you can take down a red-BioMech with a knife when you run out of ammo)

one of the perks of doing this on "Tourist" is that you get 200 base health, and 200 base armor meaning that you could in theory stop lava Golem bolders with your face, and kind of not care. the other perk of Tourist is that you get regenerating health, so if you realy didn't want to have to deal with toads, or Kamakaazies you just shoot a few of them, and let the rest hit you then have sam suck his thumb a bit before going to the next room, or triggering the next wave.

the achievement specifically bars you from using any bullets or shells meaning that the revolvers (single or double), shotgun, super-shotgun, tommy gun, and minigun are out of the question
but the rocket launcher, granade launcher, laser gun, cannon, and the knife are fair game.
normaly every weapon is a tool to be used when needed, and every tool has a different job, but when we have to ignore 5 of our 10 tools the toolbox is not that impressive, or just suicidal.
in order to progress in some levels you are required to pickup certain guns to progress, and if you just so happen to be holding down the trigger as you do you will fire, and have to restart the level if not the run. (I was super cautious, and considering that the game only tells you if you succeeded, or failed for this achievement after the final boss I was not going to check if it was the level, or the entire run that had to be restarted)
-if someone else would like to check fine, but beside very specific means breaking Valve ToS I have no way to check anyways.)

knife: the best use for this one is right at the beginning of the first level until you get the rocket launcher, and then against the harpies until you get the lasergun after that you can just forget you have a knife
rocket launcher: this will be your best friend for the first several levels, and you will be using it a lot because you will hopefully be playing below normal to remove the splash damage from your own rockets that also means rocket jumping is out of the question. most enemies you will come across will still need anywhere from in the neigborhood (usually at their feet to multiple dirrect hits
Granade launcher: by the time you get this I find it is relatively useless as the rocket launcher has a lot more versatility, and personally I never cared that the granade launcher was even in the game.
laser: this is probably the best weapon for this achievement, and maybe in the game. the only problem is that you don't get it until partway through level 6. especially with infinite ammo. you just end up running, and gunning everything down unless there is herds of bulls, or kleens.
cannon: this is mainly used for herds of bulls and kleens.

beheaded, Gnaar, : rockets near them is fine they will typically die to the splash damage. knife is 1 hit if you want.

Kamikaze: you will need to be pretty accurate with your shots with these guys as you can hit the ground near them, but if you miss the ground reaquiring is costly on time for the other ones. at the start of level 2 when you fight a bunch of them at the opening of a temple just back up into the alchove, and keep firing at the ground at the top of the ramp. in more open environments you probably need to aim for dead on chest (don't aim for the bombs it is valuable ticks of the fuse)

electro-fish: accuracy is a must as they will come right up to your face (another reason to go low difficulty)

marsh hopper: for the most part on Tourist dificulty they are just a nusence to make you lose your armor. on Oasis level you can just stand in the center of the room on the health pickup, and you will not die because your health regenerates faster then they can kill you, but that does mean you won't have any armor for later in the level. otherwise just back into a corner (near the entrance door preferably) and spay rockets in the semi-circle around the corner. you will probably still get hit by maybe 10-20, buy you should be fine.

Kleer: these will actually be the most difficult enemy to deal with considering that they are so numberous, and they take 2 hits of splash damage, and 1 direct hit. circle strafe them as much as possible, and accuracy is a must as you can still die to 5 or more of these if left unchecked.

werebull: these will take 2 rockets to the face before they go down meaning that long range as much as possible the good news is that you will not see more then 2-3 at a time until you get the laser gun, so these should probably be a higher priority then even the kamikazes as they can put you out of position so much.

biomechs: blues take a single rocket, while the reds take 4 or more depending on if you hit their rockets in flight.

arachnoids: yellows take 2 hits, and reds take 4. the worst part is that the rate of fire of the rocket launcher is slower then the stun time so you will be taking a few hits between each rocket hitting.

Retiloid: green Goro will be a annoyance every time they show up. they will take 3 hits from rockets, and dodging their projectiles multiple times is tedious. shotting the projectiles with rockets is worse the second time I encountered these I just didn't care, and let it's projectiles hit me.

harpies: these are actually the only enemies I will say just use the knife. they will land eventually, and dodging their shots can be done easily, but the rockets move so slow that the harpy can just avoid it, so it is easier just to dodge their attacks, and wait for them to try to melee you, but you basically want to run/jump/attack at them to ensure a hit.

when selecting level 1 to start the game be sure to go to custom difficulty. set it to Tourist, and turn infinite ammo on.

get the rocket launcher in level 1. (from the level start switch to the knife go up the steps. killing the guys that spawn. turn right get on the wall on your right. at the corner diagonal jump to the roof top and turn left to grab the rocket launcher.

whenever you pickup a gun (revolver, shotgun, tomygun, minigun) don't touch the trigger button until you have changed to one of the non-prohibited weapons

before you have the laser gun: Kleens (skelaton raptors), and kamikazies should probably be percicion hit instead of just in the neigberhood to prevent agrivation. and harpies should just be knifed.

once you have the lasergun (Dunes) you are basically set for the rest of the game. get the cannon in "City of memphis-Metropolis" to make the running of the bulls/kleens area so much easier.

while going for this achievement you can also do some other achievements if you don't already have them.

cannon expert: this can be done in the metropolis level durring the running of the bulls/kleens just fire one cannon shot at a time, and let the group together before firing (you might need to wait for the kleen portion as not that many bulls appear at once not to mention kleens knock you out of position less.

look, it's a secret if you follow this guide you can actually get this achievement easily by level 8 or so

Serious run: just move through the levels as quickly as possible if this is your second, or so time through the game it shouldn't be to bad save the first level. (5 minutes really)

perfect kill: I would suggest following this guide to get this (when you bring up the overlay time is paused for the game, so use that to your advantage.

I do not think that the secret levels are required to get this, but I did them as well. (you don't get any of the allowable weapons eairly by doing them, but I don't know if I could get some kind of clarification of this it would be nice.

from what I have seen based on posts by croteam the way they track the achievements for completing the game they do so by checking what order levels have been completed in, and if a level is out of order the run is disqualified, so if you beat level 5, and then for some reason go back to level 4, and beat that the run is disqualified for any of the "complete the game" achievements. secret levels are exceptions to this.