RESEARCH and DESTROY

If you have the Laserizer you can use the Max Amplitude setting and see how much life the Relic has left. Just get it to 15 and then hit it with the Kinetic Bubble and watch the achievement pop!

Very straightforward I got this on my first encounter with the relic unit. Firstly, get close even right underneath if you must it makes aiming/firing the projectile much faster so you waste less seconds thus less turns and it can't attack or hurt you. Line it up and keep hitting it directly with the launched bubble cannister. If the bubble deploys around the relic you can't shoot through it so just get as close to it as possible to avoid wasting more seconds firing again. It did roughly 15dmg per hit so a couple of turns should see him off, use your other two scientists to deal with any units the relic spawns. Possibly more difficult to achieve in later levels as the relic could pull more challenging unit types. You could also weaken it with stronger attacks first, but I didn't risk killing it incorrectly.