The Texas Chain Saw Massacre

To unlock this achievement, you need to kill a victim using an execution while playing as a family member.

In order to complete an execution, you need to strike a victim while they are low on health, delivering a strike that will kill them by diminishing all their remaining health. This means the victim will need to be hit by any family member about three times (without healing) to get to low enough health.

An execution is a finishing move that involves a little cutscene of your family member killing a victim. Once this has occurred, the achievement will pop.