Fallout: New Vegas

Achievement Hunters!

The two solutions above are good, but neither of them show the quickest way to get the achievement. The method below will take about 5-10 minutes and you will get both "10,000 damage" achievements associated with GRA.

REQUIREMENTS
Around 25k in caps. If you have this, you're good to go. You'll also probably want to make sure you have a bunch of stimpaks on hand in case you take collateral damage from the mini nukes.

WHAT TO DO
** Fast travel to the Gun Runners mark on your map (just below and to the right of The Strip) and save your game.
** Buy "ESTHER (GRA)" from the robot at Gun Runners. It is around 22k and is a Mini Nuke Launcher that counts both as a GRA weapon and a "unique" wasteland weapon.
** Buy all the Mini Nuke ammo that they have (the Mini Nuke mod for sale at Gun Runners will not work on Esther so save your caps).
** Fast travel to Black Rock.
** Make your way to the top of Black Rock killing everything along the way. There are a bunch of Super Mutant Masters and Nightkin Masters.
** You will most likely have exhausted your Mini Nukes at this point.
** Return to Gun Runners and buy another load of Mini Nukes (they will be restocked).
** Fast travel to The Strip. Kill the three securitrons at the entrance to The Strip.
** Enter The Strip.
** Launch a shot at the two hookers in front of the casino. You should kill 4 or 5 people total with this shot.
** Both Achievements Unlocked!
** Reload your save game unless you want everyone in The Strip pissed at you.

If for some reason the achievements didn't pop, open up your pip boy and find the two challenges that are associated with these achievements (Notes -> Challenges -> Hit Right a Couple of Times). They will show you how much damage you've already inflicted so you know how much more you need (if you didn't get it, you're probably right around 9900 or so).

Although the above solutions will work, I found this method much faster:

1) Earn enough caps to be banned from all 3 casinos on the strip.

2) Purchase "Esther" and all mini nukes from Gun Runners.

3) Go to kings school if inpersonation

4) Fire a nuke at the stage from the doorway to that room, restore health.

5) Wait for the radiation to disperse, then fire another nuke into the doorway leading to the stairs behind the counter (to your right when you first enter the building. This unlocked for me at this stage.

NB) I was at level 31, with an explosive skill of 67 at this point. You may need to also kill passers by outside depending on the damage your character can produce :D

This achievement can be gotten naturally, without any real effort. Any weapon that has a unique name is a unique Mojave weapon. For example, I was using Benny's gun "Maria" when the achievement popped. If you have the Gun Runners Arsenal DLC this is made very easy, considering a lot of the guns have an actual name. A large chunk of my kills were with "Bozar" before switching to ''Maria". The DLC is not required though. There are tons of unique weapons in the wasteland. I found a shotgun called ''Dinner Bell" exc... I just thought this was worth mentioning.