Achievement text: "Survive an attack due to the ballistic protection augmentation."
You need to survive an extreme amount of damage with the Ballistic Protection augmentation active. To do this, I got to full health, turned on the BP aug, and let a guard see me. He unloaded mag after mag into me, and I popped medkits and biocells to stay alive and keep the shield up. When the medkits ran out, I let him kill me. I died, and got the achievement.
I learned afterward that you can also get this by surviving multiple pistol or sniper rifle hits with the augmentation active.