Inconsistent reports - Killing Blows required, just not necessarily with the Rocket.
Soldier 76's Rockets aren't quite strong enough to kill anyone in one shot, but it does 120 damage, which will do about half hp or more to anyone except tanks. As with most multi-kill achievements, I suggest trying to pair it with a Zarya Ultimate. Other than this, the best bet for people being stacked is when they're on the payload. Save it for once you've softened them up a bit, perhaps with your own Ult.
Your rockets do auto-aim during your Ult, but they don't get guaranteed hits like you bullets do. They lock-on to where the person was standing when you fired.