I was a little daunted by it when I first unlocked it but it wasnt so bad.
First if your team is gang busters your probably not going to get it.
Second. Pay attention to the bottom left screen. This is where the game informs you who’s killing who. If you see someones name pop up multiple times. Find your teammates “X” waypoint and immediately go to the spot they just died. Do this and you may get lucky. Usually folks with swords, hammers, rockets and even skewers are the ones with killing sprees so pick up a repulser off the ground if you do not have one already.
Lastly if you can get a team of 4 together. You can just play bad on purpose. Let the other team destroy you until you see one or more on the scoreboard with 5 kills no deaths. Then come alive and get the kill. Do this until all 4 of you have it.