Perfect Dark Zero

The little trick in my video should help you get 1000 sniper kills in no time at all. It requires a second controller though.

Match setup:
Team Killcount (Deathmatch)
Map: Desert, small variant
Custom weapon setup:
In slot 1 - 4 add shield
In slot 5 add the Jackal
Bot setup:
Bot count: 14 (to allow your other player to join)
Difficulty: Agent
Bot teams: Humans vs Bots
Personality: Bully

Set the time / score limit to whatever suits you, just make sure you don't set the time limit to infinite (the game won't be able to end properly and the kills won't count toward the achievement.) 20 minutes with no score limit will get you close to 100 kills.

Note; If these sniper achievements don't seem to be unlocking for you and you have only been using one of the two snipers thus far, try earning a few kills with the other sniper rifle. For some this seems to help, whereas others have no problem acquiring these achievements with only one sniper. More info in the comments.

A much faster and easier way to do ANY of the 1000 kill achievements (with the exception of 1000 kills in killcount, and 1000 explosive kills - the current guide for explosives seems to work faster than this solution) is to set up a local match on TEAM killcount. Plug in as many controllers as you have laying around (guitar/drumset controllers will work for this too, though you can't actually move the characters with them) and set up a match on the small variant of the desert map. Set up the teams so that it is you vs. everyone else.

Now, depending on what achievement you are going for, create a custom weapon setup with a weapon of that class in the first slot so everyone spawns with them. For example, you can place the jackal in the first slot if you're going for the "x Sniper Kills" achievements, or a rocket launcher if you're going for the "x Explosive Kills" achievements. This will ensure that you'll never have a problem finding ammo for said weapon since whenever you kill someone, they'll drop theirs.

You should be good to go now. All you need to do now is set a round limit. I prefer 20 minutes or 100 kills, whichever comes first. When the round starts, all you need to do is run to the area in which they spawn and kill the non-controlled characters as they spawn. They should always spawn in the same area, so just pick them off as they pop up. I've been using only one extra controller, and I've been getting 100 kills within 20 minutes every single time. It's worth noting that I run the 2nd controller into the teleporter myself rather than waiting the 15 seconds for it to go automatically. Otherwise, you'll end up with less kills for the round.

For this specific achievement, Just make sure to use a sniper rifle. I prefer the jackal, but theoretically, the shockwave should also work. This may be obvious, but getting headshots for every kill will count towards that achievement as well.

If you have multiple controllers, then use the following settings:

Mode Deathmatch
Scenario Team Killcount
Level Urban
Level Variant Small
Weapons All Jackal (custom)
Bot Count 0
Time/Points Limit Your choice, but don't set both to infinite as the game only records progress after the match ends
Base Assignment (Advanced Options)Fixed
Spawn Type Teamspawn

You will start the game in the casino, whereas the other players will start across the plaza in the hotel. Simply walk over to their spawn point in the lobby as systematically kill them using Jackal headshots as they spawn in. You can either walk the other players into the teleporter or wait until they automatically come through to where you're standing. The only time you'll even need to move is replenish ammo. I found this to be the quickest method, and using 3 dummy controllers I was able to get around 100 kills every 20 minutes