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The New Vegas Samurai achievement for Fallout: New Vegas is worth 15 G

To get this you have to Cause 10,000 damage with Melee Weapons.

I got this achievement pretty quickly and easily by using a special weapon called the "Oh, Baby!". This is a special hammer weapon that is pretty fast and does a lot of damage. You can find the Oh, Baby! in the Charleston Cave, on/next to the corpse of a dead Nightkin (where you find the chewed Stealth Boy).

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.

If you're going after fleshy enemies (human, ghoul, animals) I recommend using a standard combat knife. It will do a fair bit of damage but swings quite fast. You also don't have to go too far out of the way for this weapon -- you can steal one fairly early in the game at the Vikki and Vance Casino in Primm.

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, "New Vegas Samurai".