This achievement is fairly difficult, because it requires you to get 15 kills (or more) and zero deaths in a single game, in a slayer gametype, on a mythic map.
Although you generally will be demolishing the other team if you're already 15 and 0, if your team does not win, you will NOT get a perfection. If you're 15-0 and the game is close, take the chance and help your team. its awful to go 15-0, and not get a perfection.
Staying alive is always key, but you must play agressive enough to manage 15 kills. Use your teammates, as they will often charge in and take plenty of fire, while you can pick off the low-shielded opponents they were fighting. If the other team is fairly decent, it will be much harder to get a perfection, so a team full of guests is usually easy to (for lack of better words..) pwnz. Try to keep the power weapons away from the other team (rockets, sniper, laser) because they tend to be really good for killing people, and when you're going for a perfection, the target always seems to be YOU. Also, keep a BR on hand at all times, and a short-ranged weapon wouldnt hurt either.
The following maps are "Mythic".
Sandbox (Mythic I DLC)
Orbital (Mythic I DLC)
Assembly (Mythic I DLC)
Heretic (Mythic II DLC)
Citadel (Mythic II DLC)
Longshore (Mythic II DLC)
[tips for each map]
Longshore is most often, if not always an objective-based gametype, and this achievement requires it to be Slayer, so VETO this map.
Citadel is a smaller map, and so it is harder to stay back and pick off opponents. I would say this is one of the harder maps to get a perfection on.
Heretic is almost impossible to get a perfection on enless you're matched up against some awful players. The map is tiny, very open, and all players spawn with 2 plasma grenades, which most people are only too eager to share with you.
Assembly is another open map, and once again it is harder to get a perfection on. The spawns can very easily get confusing and you'll probably find yourself stuck behind your enemies without a way out, and will probably die fairly easy.
Orbital is an easy map to stay alive on, but you wont get many kills hiding around behind the boxes. To get a perfection on this map you're going to need to control the map near rockets, and never try to be a hero and stick your head out when theres a hall full of enemies.
Sandbox is probably the easiest map to get a perfection on because with a warthog, mongooses, choppers, and a huge wide open area, people wont focus on you very often. This map is also easy to stay alive on because the other team will ONLY spawn on their side, either in the base, or off to the left or the right. The easiest method to get loads of kills, is to fight/sneak your way into the enemy base, and proceed to stand up top and spawn-kill them. Because they wont spawn in the base beside you, they'll be out in the open every time. If the game is Team BRs, you'll have trouble sticking up top with a BR because the enemies will be able to shoot back at you easily. If the gametype is simply Team Slayer, your opponents will be helpless against your rain of BR shots.
Another method of getting this achievement is have a decent driver drive you around in the warthog while you gun down the enemies (spawn killing if you can), but careful not to die, because warthogs tend to be huge targets.
If the host of the game leaves, or the host is changed sometime during the game, any killing spree you have or are on will be reset. However, as long as you get your 15 kills without dying, you will still get a perfection. It IS possible to get a perfection without even a killing spree.
another note with this glitch, is when the host changes or leaves, all weapons and powerups will respawn, so watch out for that.