The kills will take a few gaming sessions so my advice would be to host a session to do the weapon kills. 1 round is 10 minutes so after you guys are done with the killing ( when none of the points are captured the game goes on forever ). Then the last 2 rounds ( it's best out of 3 ) you should farm some objective points. This way you won't need to host a separate session just for the objective points.
Get familiar with hosting matches in this game, you really should read my guide for the weapon virtuoso, I pretty much lay it all down.Solution for MP - Weapon Virtuoso in Medal of Honor: Airborne
Now for the farming method.
Game type, Objective Airborne, always Objective Airbone :)
We liked the map Destroyed Village the most because it's small and is excellent for getting kills like I describe in my weapons guide.
Get everybody to one of the flags. This does NOT have to be the middle flag unlike some will claim. All the flags will give the same amount of objective points. We always picked the one in the courtyard of the church. Now if you ever done King of the Hill boosting on Gears of War 2 then you'll be familiar with this method.
Team 1 will walk up the flag to capture it, after it's captured get out of flag's zone. Then Team 2 will capture it and back out again. Rinse & Repeat. You get 1 objective points per capture and another when you neutralize it. I believe we got around 125 objective points after every weapon kills session. So when you should be done with Weapon Virtuoso you should already be very close to this achievement, might already unlocked it even.
Important Note. The more players are capturing the faster it will go. If you have someone in your boosting crew and he already has all the objective points he need, still ask him to help and join the farming. This will save time !
That's basically it.
It's been a while since I did this achievement so maybe someone can send me the correct numbers about the rounds length, objective points per capture and how much you can get after a match. My estimations should be right though. It's just that there used to be a good solution here on TA but it's gone now.