I was playing as a medic yesterday and racked up a fair few points, and I got the medic combat badge
Basically as a medic your main aim is simply healing, don't worry to much about actually firing at anyone, hang back behind a group of team mates and just nip out to shock them a few seconds after they've been killed (this gives whoever killed them time to move away or look elsewhere). Leg it over to them, dive down to lying position, shock them and then run for cover.
There's only two ways I really kill people as a medic, the gun doesn't do that much damage, so I'll either spray full auto at point blank when someone runs into me, or for the medium range kill I use the SA80 (the first medic unlock - which isn't that great) and fire single shots, it has to be single shots as the recoil penalty is huge.
Also drop medic bags in anywhere that a lot of fighting is going on, drop them on snipers lying down and anyone else firing from a fixed position, you'll get more points doing this if your team is defending, the start of Sharqi Peninsula when the US are defending is a good time to get your basic medic badge (5 heal points).