One easy way to do this is by using only one Lv5+ scout unit into an equipment collection main mission (side mission won't work, thanks to the folks in the comment section).
Here is the build I used. I finished the mission in 3 turns and collected 4/5 crates without getting any hit.
The key skills are- NIMBLE, Free Cloak, and Sprint.
Nice-to-have skills are - Extended Cloak or Regenerative Cloak, both provide you survivability.
Nice-to-have equipment is - Ranger boots and Potential-passive vest.
In the mission, you just need to find the best route for 3 crates, use Sprint for the longest straight line and use stealth cloak to avoid overwatch or melee auto-attack.Tips-
Cloak first, if the crate is your destination, because you can get 20% extra movement range under the cloak.
If the crate is 1/2 AP away from you, it's better to cloak after you pick up the crate. Because the cloak will cancel once you pick up an item, you could get hit in a bad scenario without the cloak.
You can only get one extra AP via NIMBLE, so if you are about to collect 2 crates in one turn, beware that you will end up there without cover.
First turn is normally the good turn to use Anticipation.
This solution should work for the achievement Ain't no one like me, 'cept me! but I haven't started my higher difficulty run to confirm.
Be sure your Xbox Live related software is connected to the server while doing this.
I also noticed that if you assign the Hero Scout Reyna as the only scout unit in other mission to fulfill the extra "at least 1 scout unit" requirement, the requirement was failed.