This does not need to be done over the course of a single round, or even over a single match. Getting one, or even no kills in a round is totally fine while going for this, what's important is not to die. Stand back and play support, scavenging kills where you can.
It will probably help if your teammates are in on it. They can provide a meat shield if need be, and weaken targets for you to pick off. And as always, enemies being in on it is going to help even more; boosting in a private match requires eight or more human players. I would recommend against asking to boost in a public lobby, especially for this particular achievement. If you aren't booted, you'll become a primary target.