This quest requires you to get eliminations by shooting the enemy in the head. Just like Thor should have done to Thanos at the end of infinity war!

A headshot can be tricky depending on the scenario you are in but I find have a good assault rifle for long range shots and a powerful shotgun can make a big difference.

If you have some range on your opponent make sure you build to get above them and you should be able to pick them off with a headshot, especially if you have a powerful mechanical assault rifle.

If you are up close and personal a shotgun headshot is much easier to pull off. Again if you have a powerful pump action shotgun it can make the difference to get you that kill.

Team rumble is great for doing quests that require eliminations. I would recommend jumping into one and gathering a good assault rifle and shotgun. You can choose whether to drop in and land by the enemy team to get in close with your shotgun or put some distance between you by building a tall fort and picking them off with your assault rifle. If you are eliminated you respawn with your weapons.