This is not as hard as it sounds.
Start by killing someone. Anyone.
Then grab their gun and try to last as long as you can, killing everyone you meet. If you can identify the one you got the gun from, then target them specifically.
It takes a few tries, but if you keep picking up someones gun and using it as long as possible, you WILL get it.
Good luck, it takes a little practice.
Have a buddy of yours join the game lobby your in, make sure you are on separate teams, or playing a free for all.
Meet somewhere unfrequented by most, kill your friend, take their gun. Wait for them to return, then kill them again.
This is the easy way, but for a simple achievement, it probably isn't necessary.