This is probably easier to get early on in the game, when the missions are easier. However, I think the best mission types for this are the Recovery ones, ie. missions where you need to get to a specific area on the map, then go to the extraction point.
I did this on 4.5 skull difficulty map, using a Spider mech with 8 jump jets, maximum armor and a small laser (you're not gonna use it though). I ran and jumped to the recovery site, and braced for an attack, as I was surrounded by 4 assault mechs (you may wanna save your game before they appear on the map, in case you need to resort to some game reloading). I managed to survive their attacks with just a missing arm, then I jumped away from their reach towards the extraction point and they just couldn't catch/hit me since a Spider with 8 jump jets pretty much flies all over the map.
If and when you survive, the cheevo should pop after the salvage screen.