I just finished my playthrough for this achievement, so here are my observations:
- Easy difficulty is the way to go. Ironman should be disabled, just in case. This is going to take several hours, and there's no point in losing it at hour 9 because you left this box checked.
- Disable the tutorial for sure, as this gives you a chance to bring home everybody from the first mission. I don't know if the first mission is counted, but I went ahead and picked one of the four from that mission anyhow.
- Since avoiding injury is the name of the game, pick someone who will hang back. I used a sniper with squad sight - I'd almost recommend starting over from the beginning again if none of your initial four turn out to be sniper class.
- Give this person heavy armor + any health bonus items you have access to. Titan Armor + Chitin Plating = less chance of medbay time.
- I gave them a nickname like "Required" or "Achievement" so I knew right away if they were in the squad. If you've got the Elite Soldier Pack, you might also consider coloring them differently.
- Psi training is pretty much out - it takes 10 days, and I've found it extremely rare that I go 10 days without a mission.
The early game was the trickiest part - at the beginning I actually had 3 soldiers who had been in every mission, just in case. However, once I had squadsight and a plasma sniper rifle there wasn't much left to do but win.
I played the game to delay the assault on the alien base until I had done almost all the research I possibly could. The enemies are pretty easy prior to the mind controlling aliens showing up, so this reduced my risk of injury or death. This took a bit of panic management with satellite coverage, but this is Easy difficulty, so it was nothing major.
Once I assaulted the base, I pretty much beelined the story missions and required buildings in order to get to the end as soon as possible.
I didn't have to skip any missions - my sniper never ended up in the medbay, and everything went fairly smoothly on the whole. The achievement popped for me when I was at the closing statistics screen.