This milestone quest requires you to get assists.

You get awarded with an assist if you damage the enemy player but a teammate does the final piece of damage so they get awarded the kill.

This requires you to play a game mode where you are on a team and should come naturally if you regularly play with a squad. Just do a couple of shots of damage and wait for a team member to finish of the player. This could back fire though if the enemy player manages to eliminate your team mate.

Team rumble is also a good option if you want to get this quickly. You have lots more enemy players and a lot more teammates so you will be able to go round and deal some damage to enemy players. They will be eliminated eventually by a teammate and you will get the assist. It helps if you are on the edge of the circle with a good assault rifle as you will be able to pick of most players and deal a couple of shots of damage.