This badge seemed impossible, untill i mastered the Jihad Humvee. I finally got my Basic Explosives badge, and with the same kill recieved a good conduct ribbon. Not too shabby, i managed to get 14 kills on Karkand, all with C4 and didnt ruffle a single good guy feather.
I got mine on karkand, bundled with the GCR as well - though I did it by mining the wall of the southern most flag with three C4, and then 2 C4 inside, and hiding. N00b tankers/APCers will always pull up to that wall because its in the flag radius... on two occasions I had a tank with an MGer up top AND an APC pull up and sit there - BOOM, 3 kills in 1!! Brilliant. What you need is a sympathetic commander who'll drop you a supply crate nearby so you can just keep topping up on C4, and boobytrapping it. Works just as well with infantry (in fact, with infantry it works on any flag) - just stick some C4 around the flag pole (try and not make it too obvious though), and if you're lucky you'll get a whole squad!! I did that on Sharqi - it was hilarious