To get a Perfection, you must win a match with at least 15 kills and no deaths on Slayer. Note that it is not necessary to get the Running Riot medal to get this achievement, someone may quit the game and your spree might be reset, but as long as you can get 15 kills with no deaths, the medal and achievement will be available.
This achievement is worth 25 Gamerpoints. It is represented by the outline of a silver hexagon on the outside, with a smaller hexagon in the center.
Another way is to try to stay back and let your teammates do the work, and occasionally pop out to finish off someone else's kill. On Sandbox just hide behind the structures and obstacles and eventually this achievement should unlock. To make it easier to survive, try to always have a bubble shield or a regenerator on sandbox. Utilize the rockets for quick and easy kills as much as possible, and watch out for the enemy warthog and players wielding rockets. Always be patient and don't be rash in order to better survive. If you do get to fifteen, you may consider hiding behind your base and waiting for the game to end.
It is also possible to get a teammate to drive you around in a Warthog circling the map, just do not go too far out otherwise the Guardians will kill you, and not too far in, as there is a risk of getting blown up with a rocket launcher.