**I would like to point out that at this point in time I do not have this achievement yet but these are my findings doing some basic trial and error.**
It would appear that all kills and assists in "Missions" and "Brawls" count toward this achievement.
In my opinion the best setup for this achievement would be to stick as many "Sidekick Drones" as possible on your vehicle and to then play "Missions" keeping a fairly low power score so that you face weaker enemies. Sidekick drone deploys a small drone that drives around and shoots a machine gun at enemies for a period of time. The reason these are great for this achievement is that if each of your drones (up to 5 on the best cabin with the best generator) shoots an enemy that later dies you will receive 1 kill assist PER DRONE that injured it. (1 extra assist if you damage said vehicle with your own weapons or melee attack but I find it better to hide behind something and deploy your drones.)
From my testing it would also appear that bot kills and assists count towards this achievement. (Bots have basic names in missions such as Ashley, David, Connor, etc.)
Using 4 sidekick drones I have finished games with 13 assists which is much more than you can obtain just shooting at enemies with regular weapons.
To view your progress towards this achievement click on your Gamertag in the top bar of the main menu, then go to "Medals" and from there go to "Missions" the "Assassin" medal is at the bottom of the list.