Small story spoilers:
At the beginning of Chapter 13, you'll go into battle with just Bolverk and Folka against a group of about 7-8 enemies. You look incredibly outnumbered but this scenario is actually ideal for this achievement. Before pressing "Ready", place Bolverk as close as you can to the nearest foe. With your first turn as Bolverk, approach that enemy and use his special ability Cull The Weak on him. It should kill him, and if so, grant you another turn. Repeat this process, moving enemy to enemy until you've dispatched five of them. The achievement will pop right away, even if your turn is still ongoing.
Hint: I was playing on easy at the time, so if you're still struggling to kill them all with one hit like this achievement would require, try playing on that difficulty.