MechWarrior 5: Clans

This one is a lot more complicated than it seems because the game is a liar when it comes to teammate health percentages. Frequently allied teammates will have more HP than the game lets on leading you to finishing missions and seeing an infuriating 23% remaining on the post level screen.

Your best bet for this is to start a new campaign and complete this on the first mission. Complete the mission as normal (I recommend switching the difficulty to Story Mode so you don't get swarmed), then once the mission has progressed far enough that the Killers dropship cutscene plays, order your squad to defend a position on the other side of the Union dropships out of line of sight of the Killers squad. This will keep them in place and help you teamkill. Your target is going to be Ezra in the Mist Lynx. Chip away at him with the pulse lasers until one of his mech legs and both his arms pop off. Now you're going to want to switch back an forth with Ezra so you can see how much armor and where to shoot next. Slowly chip away him with a single(1) pulse laser until he gets to under 20%. If you kill Ezra or he has more than 20% armor remaining you'll have to restart. When the mission completes and he is 20% or under tab over to the Repair tab and dump all of your research points into upgrading your repair techs until it says that health for next mission is 100%. Once it does simply start the next mission and it'll pop after a few seconds. o7

Don't be like me and think this can only be done mid-mission, as that can be nearly impossible (the repair bays won't always get you to 100%, based on components lost in battle). Take any 'Mech with machine guns and whittle down one of your partners at the start of a mission. Take off both arms and one leg, then carefully shoot the torso until you get to 19% - if you leave them at exactly 20% they may end up at 21% at the mission resolution screen later, presumably based on weird rounding or something. Use the Battlegrid to order that 'Mech into a corner away from everything else and then roll the rest of your star out to complete the mission. Once finished and back in the 'Mech Bay, make sure five repair techs are assigned and the "HP to next mission" box in the upper right shows 100%. Then go start your next mission and the achievement will pop.