The Mechtoid is a Sectoid in a Mech suit, when another Sectoid mind melds with one the Mechtoid gains a Psi Shield (6 HP) instead of a 1 HP normal health buff. Also unlike with a normal mind meld, killing the Sectoid generating it reportedly doesn't kill the Mechtoid (apparently it drops the shield and inflicts 3 HP damage to the Mechtoid - I haven't personally confirmed that)
The good news is that this achievement is just for the same turn, it doesn't have to be for the same shot. You can have your whole team light up the shielded Mechtoid and as long as it dies in the same turn you kill the shield you get the achievement.
In my case I'd damaged the Mechtoid in the previous turn, before it got a shield. Then my sniper hit the Mechtoid, knocking down its shield, and another trooper actually killed it (IIRC with a light plasma rifle).