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15 G

Cause 10,000 damage with Unarmed weapons.

I got this achievement pretty quickly and easily by using plain-old Spiked Knuckles. Insects are very vulnerable to blunt weapons -- one way to speed this up is to fast travel between the various dry lakes in the game, you'll encounter quite a few ants, fire ants, and smaller radscorpions at those locations. Just wail away, keep an eye on your health, and you'll get this in no time.

Feral ghouls are another good enemy type. Nightkin are decent, as they usually get pretty close before they drop cloaking and shoot, making them a viable target. I would avoid trying for this against anyone with a gun, a clear line of sight, and room to move. If you're going to do this against guys with guns, do it indoors.

To track your progress, go into your PipBoy, press RT to go to "Data", left stick over to "Misc", press Y for "Challenges", and press X to show "Damage Challenges". Look for, of course, "Old Tyme Brawler".