Fallout: New Vegas

You can get this achievement if you go through the game using explosives. Most people dont (like me) so heres what i did.

I went to Black Mountain (there are some supermutants and nightkin there) to get the companion Raul. I got a Missile Launcher from a nightkin on the tower there called Anabelle. Its fairly good and cheaper than buying one.

Save your game and turn hardcore mode off, this while allow you to carry a ton of missiles. I bought like 100 of them from the Gun Runners (50 high velocity and 50 other ones with a bunch of normal ones).

Now go kill EVERYTHING. I suggest hittin up Jacobstown, and any other place you know with super mutants and nightkin. They have alot more HP so you can rack up tons of points toward your 10000 dmg. after wipin out the Legion Camp i got about 2500/10000 and that was for killing like...50 guys. After killing jacobstown i was up to like 6200, and theres only about 12 supermutant/nightkin there. So there you have it. wipe out vegas if you have to as well, robots are good too.

GOOD LUCK....with this game...grrr

This achievement is easy to earn if you use the right tactics. Turn off Hardcore mode, and you might want to consider changing your difficulty to "Very Easy", as you deal more damage. After this, you must collect your munitions.

Ammo, certain weapons, and grenades can be stolen from the Boomers in the mess hall/munitions storage hangar (no negative rep as long as you are hidden when you hit the "steal" button, click RS to drag items into hiding with no penalty). More munitions and ammo can be purchased from Mick in Mick & Ralph's or from Vendortron at Gun Runners. Next, you must acquire your target.

I would suggest going to Gomorrah with a missile launcher and grenades and slaughtering everyone, especially in the lower lobby (as all the gamblers funnel out and can be killed with one rocket). I think that murdering people on the Strip is the funnest (and possibly easiest) way to earn this achievement. If everyone on the strip is dead, yet you do not have your achievement, try some other densely populated places, like The Fort, Nellis Air Force Base, Jacobstown, or any of the NCR camps.

I would NOT recommend using the Fat Man, due to the fact that the ammo and the gun itself are very expensive, and in the tight spaces, a missile launcher can actually get the job done better, due to the straight, fast flight path and pretty good damage.

Good luck with this achievement. It took me all of 15 minutes to get, and I enjoyed every bit of it.

I got this in about 45 minutes, on very easy mode. All I did was use a Grenade Machinegun with 2700 rounds and my explosive strength was a 31. Keep in mind I was level 29 also. I went in front of the Lucky 38 and just started shooting everything I saw than I went through the Gate to New Vegas Strip did the same thing by the Tops and repeated the process. Securitrons will respawn everytime. I shot all the Securitrons in the face and when I got the achievement I had 1947 rounds left. I also only used 54 Stimpaks with my medicine set at 35. Good luck and I hope this works for you.

This Achievement isn't as hard as it looks but it can take some time to unlock. Ok so there are many methods on getting this but the way i got this was obtaining two explosive weapons. The first is a Rocket launcher called (Annabelle) the second is a Grenade launcher called (Thump-Thump).once i got these weapons i made a another save game so that i wouldn't mess my progress up. once you feel happy with your weapon layout and have enough stimpacks you can proceed to the Mojave and just Shoot everyone and everything.

These links are to help you out to find the weapon and to also learn a bit more about each one

(Annabelle)
http://fallout.wikia.com/wiki/Annabelle

(Thump-Thump)
http://fallout.wikia.com/wiki/Thump-Thump

UPDATE: Frags and plasma grenades also a good thing to use
(thank u TragiK x SlayeR)

All of the above works but I went into the quarry with my missile launcher and took down all the deathclaws then went to black mountain and killed all the mutants.

I found a very simple way of getting this achievement, but it costs quite a bit of money(Because of how expensive C4 is), it requires you to finish a long quest chain, and you'll probably be near end-game by the time you can do this.

I had problems using Thump-Thump or any grenade-launching guns, mainly that after the first shot the explosion nor direct hit did ANY damage to the enemies, just to me, so I had to find an alternative. Then I realized I had some C4 stored back in my Novac house and decided to do this.

First off, you will need to have finished Red Lucy's "Bleed Me Dry" quest where you collect eggs for her and you get to fight the monster whose egg you collect. Once you collect the Deathclaw egg, turn it in, get some loving, then it's time to start.

Go to where Red Lucy is and fall off the top-left corner into the battlefield. Go straight to the portion where the enemies spawn and drop TWO C4 at the edge, right next to the sliding door. You would probably only need one if you had 100 Explosive or were on Easy/Very Easy.

Now, just go to the middle-right gate, open it and go up the stairs to Red Lucy and choose these options:
I want to know more about the Thorn --> I want to fight --> I want greater challenges --> I want to fight Deathclaws --> Bring them all on(Or whatever the first option is called). Then it's as simple as turning on Sneak and Sneaking into the arena. Once you see THREE Deathclaws(There will only be one but then they'll separate like clones once you get far enough into the arena) just detonate the C4. If you placed the C4 right next to the sliding door and are sneaking it should instantly kill all the Deathclaws.

You get about 700 - 900 Explosive damage each time you do this, but the downside is that it costs about 2500 - 3200 Caps EACH TIME you do this because of the C4 you throw. If you're starting from 0 this will take at the very least 26. At the very least.

Additional information:
I was level 30, had 20 Explosive(18 with a buff) and 100 Sneak when I was doing this. Only took me about 18 C4 with around 2000 damage gained from messing around with Thump Thump previously. Took about 20 minutes total to get the achievement.

a quick way that i done this was i bought the grenade machine gun and ammo. then head to the bommer base and completet the ant misbehavin quest (if you have then it dosent matter) as you can get a good amount of damage from the giant ant now save it. if you don't want your rep to be changed by bommers then go into the mess hall and just spray and pray you will rack up damage quickly but now before going back outside search the bommers and take their wepons and ammo and then go around the rest of the base killing everone (you cant kill the kids so don't waste ammo on them) and just repeat the process of killing and picking up ammo if your achivment dosent pop then just head to new vegas and into one of the casinos and kill most people by this time you should have done it.
*i had about 4000 points damage when i went to the bommers so i got aroung 6000 points then my achivment came so if you have less then you should be prepared to go to the casinos but i don't know how much damage this will give you* lastly i also done the quest ant misbehavin i think you get about 500- 1000 damage depending how many you kill. hope you enjoy the achivment.

I found it very easy to get this achievement by playing "The lonesome road" DLC, and acquiring the Rockets Red Glare with all the upgrades. If you complete the DLC using only/mainly the RRD, you should finish with at least 8900 damage. Then just go around and kill some random creatures for a while and BAM! Achievement unlocked

I found a very easy way to get this achievement instantly.

Make sure you have a Fatman and a mini-nuke (1 is enough) that does a lot of spread damage. You can buy this at the Gun Runners store (sold by that robot). It normally sells 3 types of mini-nukes, one of those does a lot of spread damage and that's the one you should be buying.

Go to the Hidden Valley and enter the BoS bunker. Go to the shooting range and go as far as you can down the shooting lane right in front of you, so you are positioned directly towards the open door you just came through.
Wait for the patrolling guard to come near you and kill him (rifle, plasma gun,.. whatever. Just make sure he dies in 1 or 2 shots). Everyone will be on alert and will stand near the opening of the door. Wait a few seconds until a group of guards will be standing there, equip your Fatman with the special mini-nuke, and fire away.
Everyone (/thing) will be destroyed in the blast range, you should normally be barely alive (I had 2 bars left, with NO armor equiped).

The achievement instantly popped up, meaning I did more than 9800 damage (I had around 200 when I started this).

I personally found it a very quick way.i had bought a fat man mini nuke launcher, i proceded to go through the main quests at hoover dam and made sure there were plenty of people on the dam first.climbed up the towers on the dam and within 7 mini nukes shot off i was past 10k damage within maybe 5mins.i realize many ppl dont wanna waste the money on a fat man but this worked the easiest for me while playing through for other cheevos at the same time..good luck to those who try it out :)