The wording of this achievement can be misleading. What you need to do is kill both arms within 12 seconds of each other and the defeat of the two arms needs to be what actually kills the boss. So, the best way to do this is to get the left arm to around 30% (be careful not to AOE too much and kill it!) and continue to kill the right arm until the body is at 30%. At this point, take out both arms and it should destroy Kologarn. You will not get credit if you kill both arms within 12 seconds of each other and then continue to kill the boss.
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