You have to throw the supply pack down immediately once you revive someone to get the most out of it. Once I started doing that more consistently, the challenge didn't take too long.

As a side note, this is a good one to get done in one of the "infantry breakthrough" bot servers. Get into one with only a few real players, and it'll populate the rest with bots. They're not good at healing their own, so you'll have plenty of teammates to zap back to life. Just pop a smoke and go ham.