Before you finish a mission, friendly fire a mech down to under 20%. Remove all armor and damage structure. Do not completely destroy the Center Torso or Cockpit and also leave one leg. Once this is done, put that pilot on guard duty out of the way for the rest of the mission. When you complete the mission and the damage screen shows you mech at 20% or less, you are on the right track.
Move onto the next mission with the mech repaired to 100%. Once you complete the next mission the achievement should activate.