Fallout: New Vegas

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".

I found the easiest way to get this for me was to get the paladin toaster which can be found at black rock cavern. then i just went to jacobs town, everywhere on the strip hidden valley and just killed everything till it popped. the video below shows where to get the paladin toaster.

credit for the video goes to atomicproductionsap

if you are planning on snatching all these weapon acheivements then this guide should help you in solving the unarmed acheivement. Firstly when i got this acheivement i had not upgraded any of my unarmed stats so i was very poor in hand to hand combat but i have found this weapon which makes it so much easier. Using this guide though will make ceasers legion hostile so thats just a quick warning if you dont want to annoy them. If you go to ceasers main camp where he dwells and with a companion and your best melee weopon or gun (whatever you prefer which you have high skills in) to kill all the gaurds when i got to the tent with ceaser all his bodygaurd were armed with ballistic fists and ceaser had a displacement gauntlet. I found killing them all very easy because they blocked the doorway so they couldnt punch me after collecting from the corpses the weapons. I started travelling the wasteland killing any enemies and just completing quests as normal it only took a little while untill i got the acheivement i also had enclave power armour which just made most bullets have hardly and impact so if you try to aim for this take some good armour.

the ballistic fist is basically a variant of a power fist and it should take roughly 2 punches to kill a standard human not sure on animals or mutants but roughly the same. this is my first acheivement guide so im sorry for any mistakes in my english and please leave any comments of how i can improve it, anyways happy hunting.

1)Turn off hardcore mode if you have it on.

2)Get the presidential suite in the lucky 38.

3)Have 2 companions (the best would be rex and lily because of the health but it goes with every companion).

4)Have a unarmed weapon who you like or the bare fists it doesn't matter.

5)Dismiss the 2 companions and tell them to wait in the suite.

6)Go to the companions and punch them until they are nearly dead.

7)Recruit them again and knock them out.
Wait until they stand and dismiss them again. Punch them again, rinse and repeat until you get the achievement.

This goes with every of the damage achievements as long as you don't kill them if they are not in your party.
I hope this helps.

the love and hate spiked knuckles was my best friend for this achievement.. it like never needs to be repaired and it kills ppl in one hit.. i jus saved then went around punching everyone.. i went to the house of impressions, jacobstown (the super mutants and nightkins helped me get this fast cuz they barely hurt me and i jus kept punching them adding up my damage) the fort is good too but they are a little tuff since they use power fists, i would stay away from hidden valley unless you were trained to wear their armor becuz they can kill you real quick with their gauss rifles

the love and hate spike knuckles can be found in bonnie springs.. zone [1.20]
on the viper gang leader

Just to add to this solution.. With the ballistic fist I got this achievement in 10 minutes. I got a lot of stimpacks and super stimpacks and some heavy armor. I saved my game file just so I could go back to regular game play afterward. Went into the hidden valley bunker and killed all brotherhood and scribes with the ballistic fist, healing when necessary. I held up in a room and let them come to me and hit them with power punches (hold rt.) Tons of damage by killing these guys. Hope this works for everyone. Worked for me.

The best weapon I found for this ach was the 'love and hate' knuckles. Have on metal armor (or better) and plenty of stimpacks and away you go. Only took 45 mins...... Best places to go are El Dorado Dry Lake , Iwanpah Dry Lake . Scorpion Gulch . As all enemies there are vulnerable to blunt attacks. HAPPY SLAPPING

All of the other guides are just fine, but I wanted to post what worked for me and didn't really require me going out of my way to get it either. I was able to get this achievement naturally in the course of playing the game without having to go on a killing rampage and reloading a save very easily.

In my case, I was able to get this completely in the Old World Blues DLC world (IE: Big MT). Early on in there, I picked up a Saturnite Fist (2 actually) and used them through X-13 and some guys outside as I ran back to X-8 for the 2nd runthrough with the nightstalkers. Using the Saturnite Fist, I was able to get all 10k damage in about 30-45 minutes of gameplay time as I naturally progressed through the quests there without going out of my way.

There are a lot of good weapons in Old World Blues that can be used towards the other damage achievements as well (Proton axes for melee, Sonic Emitter / LAER for energy weapons, etc).

I did this very quickly only visiting TWO locations and despite my low Unarmed skill (26).

1) Turn game to VERY EASY.

2) Equip/Use the "Pushy". (http://fallout.wikia.com/wiki/Pushy)

-Yes the "Ballistic Fist" does the most DMG of Unarmed weaponry, but the "Pushy" has the highest DPS. It also has a higher HP (120) and lower Strength requirement (2). But the most useful effect is that since this is a unique "Displacer Glove", it has a knock-back effect. This opens up two advantages for those with low Unarmed abilities following the first strike:

*Allows a "bum-rush" to a second strike to kill the enemy before they can re-establish themselves. :)
*Allows you to back up around a corner/into cover to bait your opponent into chasing you. You can then spam the VATS button as they round the corner before the AI can "actually" see you, giving you free two preemptive strikes. >:}

3) Load a game where you are on good/neutral terms with the NCR and Legion.

4) (OPTIONAL) Have 2 outfits with one being NCR faction and the other Legion. It might not make a huge difference, but this is how I did it and figured it couldn't hurt!

5) Disguised in your Legion apparel, fast travel to "The Fort". Sneaking behind everybody here [HIDDEN] and attacking with your "Pushy" should one-hit KO most enemies. As a plus, nobody will turn hostile. When I got to Caesar's tent, it was not feasible to remain [HIDDEN], so I just had an all out brawl that was fairly easy. Now if needed, you have a good amount of "Ballistic Fists" to use for repair (if you have the Jury Rigging perk), or you can use the "Displacer Glove" that Caesar drops.

6) Disguised in your NCR apparel, fast travel to "Camp Golf". Repeat what you did at "the Fort". Even better here, alot of the NCR will be asleep in the tents, allowing a controlled environment for racking up the damage undisturbed. I got my achievement before I finished wiping out the entirety of "Camp Golf" without anybody turning hostile. I assume if needed, you could go inside to the main building where all the Rangers stay and get the remainder of your necessary damage.

Of course reading Boxing Times, having perks, boosting stats with apparel, and Stealth Boys are additional bonuses. If you still need an easy place to rack up some kills, try Vault 3 where the Fiends and Moto-Runner reside. They're easy to kill, plus the confined spaces will benefit your Unarmed attack. I would've done this, but I had already wiped out the area earlier. :(

1) Turn the game down to Very Easy.
2) Grab the Ballistic Fist or any proper weapon of your choosing. Ballistic fists can be found at THE FORT where ceasars legion resides. Inside the weather control room behind and to the left of ceasars main tent. Also inside ceasars tent.
3) Travel to THE STRIP and go on a rampage. Once your done fast travel to any other location thats outside and go on rampage. I chose NCR outposts because they have a good amount of people and you can then fast travel from them instead of entering buildings.

This same strategy may be used for the melee/exploision/energy/etc achievements also.