I got this by smashing a goblin with another goblin.
The achievement doesn't actually require you to kill with the improvised weapon (It says it in the name of the achievment but the description doesn't necessitate it).
It's possible that it's easier to achieve if you don't kill, since there's multiple damage sources in the attack that might disrupt it (I.e. If you kill with "Crushing damage" of the enemies weight, then you've hit a corpse with an enemy, not an enemy with an enemy)
Try picking up a full health goblin and smacking another full health goblin and see if that gives you credit.
Thanks, but that was exactly what happened. I attacked the 2 guards at the west gate of Moonhaven. Lae'zel picked up one, and smashed the second (who had 9HP I think) with one blow.
