In order to earn this achievement, you must earn Five streaks of Five kills in PVP in Elimination or Skirmish, the two deathmatch modes. The five streaks can be done in multiple matches but you must do 5 kills in one match without dying to progress on this cheevo. This means you CANNOT earn this in the following:
-Player vs AI
-Dominion or Brawl modes
It takes a lot of practice and a little bit of luck, because if you happen to be ganged up on, you're as good as dead. It's also worth noting that they must be kills, and CANNOT be assists. Unfortunately they show up as Takedowns on leaderboards, so just track it through the Achievement tracker and make sure it comes up "Your gamertag killed opponent" on the bottom left screen, otherwise it won't count. My advice would be to:
-Always attempt this in Skirmish. Elimination rounds were too short to me, and you can be partnered against a skilled player who may take you out. You can set a preferred match type in the menu and although not 100%, you can often get put straight into Skirmish
-If you start to take damage, run to the hills. If you look in the minimap icon in the corner, you can see icons which give boosts. Look for a health icon, but make sure it is white and not hollowed otherwise it'll be useless. Other players may give chase, just utilise sprint and dodge to avoid them.
-Character choice will make the difference, and make sure you upgrade your gear, level up your character a bit and find the best one for you. Nothing is worse than going into a battle with an underequipped character who you're unsure how to use.
-Make sure you learn the combat system, if you aren't blocking, parrying and countering properly then human players will make mince meat out of you.
-You can also vote for a map after every match and you can vote for a skirmish match to ensure you get that mode.
It took me a few games to earn this legitimately, so patience and perseverance is needed. I'm not sure if it's boostable, but if so then I recommend you find other players to do it.
Thanks to iVale and RagingXero for offering extra tips which Ive added to the guide