The information on the other solutions is correct, however none of them seem to explain the best way to boost this achievement. There's barely anyone playing this game anymore so boosting has become a necessity. First let me start by giving you some stats.Time:
This achievement alone will take you around 10 hours, which isn't so bad compared to most FPS games with their ridiculous kill count achievements. Take in consideration that it will massively help if you got boosters with you who know what they are doing. Kills needed:
300 for each weapon type, 5 weapon types which make a total of 1500 kills.
Ok so first thing first, for this particular achievement it's best if you boost this with 6 people including you. You can do it with 4 but 6 is the number to go with. Now by far the hardest thing about boosting this achievement is the matchmaking, it's terrible. The most important thing, to avoid wasting time on matchmaking is to host the sessions at the best time. The best time to be hosting these sessions is in the afternoon GMT Timezone. A lot of us work so if you are doing it in the evening go for 6 or 7 PM GMT.
On to the Match Making itself. Tell your party to select Ranked Matches > Custom Match. Set the map to "Destroyed Village" and the gametype to "Objective Airborne". As the session host make sure everybody hits "search" at the same time. You'll see a message screen saying "pooling players" now just cross your fingers and hope you'll all end up in the same game. Most of the time this takes a few tries but you'll eventually end up together.
The boosting. The method I used is probably the most safe to go with so let me explain. You'll see a timer in the right corner of the screen, don't worry about that. Just let it run out and the game will keep going in "Sudden Death" mode. As long as you DO NOT capture any flags, the game will keep going on for as long as you like. Pick 1 person on each team who will go for the kills first, word of advice, go for 50 kills before changing the player.
1 player on the Allied time will go to the entrance of the church and stand right in front of the door, do not go into the church ( only for ammo ) because it will mess up the spawn points. The 2 players on the Axis team who are not going for the kills will run for the entrance where the player from the Allied team is waiting. Kill them through the door, while they are inside the church. Re-spawn, and repeat until you get 50 kills. Then change player.
The player on the Axis team who is going for the kills will simply stand outside next to the church. The 2 players from the Allied team will need to steer their parachute right in front of him so he can kill them. Repeat until he reaches 50 kills.
The 2 players that act as free kills should ask the person going for the kills what weapontype he uses, and equip it, that way he can pick up your ammo.
When you're all done, simply capture a flag and the round will end. Capture the flags on the next round to end the match. IMPORTANT ! DO NOT close the stat screen, this is the part where your kills will be saved. Let the 30 second timer run out and as soon as your back into the main menu, your kills are saved.
The reason I'm doing 50 kills each is because you'll be prepared if something goes wrong. If someone needs to leave all of the sudden, or if someone drops ( god forbid, it can make your kills go to waste ) then you won't have to catch up on a lot of kills to even things out.Important Information
If the host will lag out, the game will end and everybody will lose his kills. So it's up to you and your party if you are going to take the risk and just stay in the same match for 2 hours. I did it like 8 times and it has never happened to me, but I've spoken with people who lost 200 kills because the host lagged out, so be warned. There is no way of telling who the host is unfortunately.
pointed out that it is possible to tell who the host is ! It's the first person to enter the game, obviously you can tell you're the first person because you will be in an empty room, you'll see others joining.
Good luck and feel free to ask me any questions regarding boosting this game.