Since I cannot write a complete solution for the entire story I just want to provide some information and advice.
"Without losing a single crew member" means you are allowed to use a medikit on someone that goes down during fight. So you can only void the achievement if you let one of the characters bleed out completely.
EDIT: According to Pilule 95, if you mind control an enemy and then kill him while he is still under your control, the achievement will not unlock. I have not encountered this problem as I only used Magnus for a couple of fights in the entire game.
The iron mutant option:
1. does not let you save the game manually
2. enables permadeath: if all characters die in a fight, it's game over.
So on iron-mutant the game will only save:
1) at the end of a fight,
2) when you travel from one area to another
3) each time a new enemy turn begins.
If you accidentally trigger a save during a fight that you know you cannot win (maybe because you were trying to take out someone silently but got caught) don't despair. There's a trick, used in many other games, that have saved me multiple times. In fact I even used it to unlock this achievement. The first time I reached Eden it gave me the other iron-mutant related achievements but not this one. So I used the trick, played the last couple of rounds of the previous fight again and when I entered Eden the achievement unlocked.
So when you trigger the save you don't want, press
on the game tab, go to Manage game and delete your save from the console. If done correctly, the game will not be running anymore. When you restart the game it will load a previous save that has been synchronized to the cloud and you'll have lost 15\30 minutes at maximum. Better than start the game over a single mistake.
Keep in mind that each time that you close the game the last save will be uploaded to the cloud. So when using the trick, NEVER close the game. Just press the guide button and then the manage game option.
And finally some game-play tips.
The most important one is: be silent as much as possible, always.
It is basically a stealth game. Even a 3 vs 3 or 3 vs 2 can be lethal if you have not prepared the fight. Always try to take out enemies silently one by one with silent weapons. Scout the area and make sure that the enemy you are about to attack is not inside any other enemy's circle.
For this reason you want to upgrade the silent weapons first. There are only three of them.
You start with the crossbow on Dux and Selma will have the ancient pistol equipped when you find her (pretty soon in the game). The final silent weapon is the Mimir pistol, which is found in the "Fallen Angel" level, where pretty much every enemy is.
As for the mutations, I focused more on the skills than the stats. Some abilities are very very important. For example, Bormin's charge is very useful because it will disable an enemy for two turns, thus allowing - for example - to take on a guy that you wouldn't be able to kill in one turn, without him alerting everyone else. Also Dux's and Farrow ability to disable robotic enemies is very important later on. Magnus mind control and Selma's root are helpful in some occasions but I pretty much always used Bormin, Dux and Farrow.
Other than that you also want some skills that increase your critical chance, like the ones that give you the bonus when you are on high ground or hidden.
As for the Pripp's artifacts, I really think the most important ones are (in order) the grenade damage, the EMP grenade effect extended for one turn and the +1 damage on all weapons. Once you have these I would go for the bonus 10% chance on mortal enemies and then on robotic enemies.
Keep in mind that you can reach some of Pripp's artifacts even without clearing the entire area. For example you can take the one in Scrapland without fighting the tank, Deathfinger and all the other guys.
If I can help with something else, please write me a private message or comment the solution.