Get into a Karkand server (preferably 32 since there's a lot less vehicle action) that has very few players in out, maybe around 10-15. I got into a server like this and got 19 knife kills in one round (but I didn't have the 100 global kill requirement then for the badge ). But that's not really a necessity, in a full 32 Karkand server with full-on action I still managed to score 17 knife kills (AND I WOULD'VE HAD MY 18TH AND EXPERT BADGE EXCEPT MY SQUADMATE SPAWNED ON ME AND SHOT THE GUY I WAS ABOUT TO KNIFE--MY TARGET WAS STANDING STILL TOO ). If you know that there's an enemy capping a spawn, run in and knife him before he knows what's going on. It's also good if you're on MEC and your team is doing a good job at keeping USMC back, you can knife your way through the alleys and even get up to the front USMC spawn and knife them as they spawn. Go sneaky. Take the side routes and come around behind those advancing. Unless you get blasted by someone behind you, you're bound to get a kill this way. Also, make sure you're a medic, then you can heal yourself if you took some hits and you'll have the long sprint (sprinting is essential).
Tips on the actual knifing:
-This is the one time I advocate bunny hopping. If you can get them to unload their rifle and pistol clips, then it's knife to knife and there's less chance of you getting 15 rounds in your torso.
-A great tactic is to jump and go prone. This propels you forward a good distance and makes you hard to hit. If you're close enough to the enemy when you see him and you do this you can slice him before he can even let 5 rounds off.
-If someone is prone, crouch above them to make sure you'll get them. No good to stand on top of them and miss to have the sound alert them.
-If someone is moving, it seems you have to slice from a tiny distance away to get the kill due to lag, don't go so close to them that you're touching them. If someone's stationary, you have to go up right next to them.
Hope these will help you.