Obviously there are several ways to do this but I found this to be both easy and enjoyable at the same time.
The point is to get 100 kills with each of the 5 starting weapons. Note that the kill counter stands on its own in versus in which the medal has to be achieved. So the kills from horde do not count.
-Start a private versus match and select Capture the Leader. -Set it to 15 rounds with the capture time on 60 seconds. -Set it to casual for easier performance. -Make sure you have your starting weapons selected on the ones you wish to lvl first. -You can play on any map but I found the map Mercy to work best since it's open. -Before you start the game, go to map settings/customization and replace all the weapons with the one you are about to lvl. Now there is plenty of ammo too.
Now since this gamemode will last for ages you will have plenty of time to get kills with the desired weapon. Enemies keep spawning and you can keep killing. Now you're team is not completely stupid so they will sometimes capture the enemy leader but no worries since you will have 14 more rounds to go. And if you run out you can always start over.
Once you finish with a weapon, just die and change your layout. Or if you think you might get ammo problems, startup a newgame and change the weapons to a different weapon.