Update: There seems to be a glitch where playing Arms Race gives you two matches played when you only played one, while Demolition only gives you one match. This could be as it detects the MVP for both teams regardless of the winner resulting in the match duplicating, which means that it takes only 2,500 matches compared to the original 5000 if you play Arms Race. This appears to be a glitch and would appreciate confirmation, also with the rumored Map Packs coming in the future I wouldn't be surprised if they fixed this in a future patch. There have been reports with players only getting one game at a time instead of the glitched two, there's still no confirmation on what triggers this glitch.
You are allowed to play Offline against bots for this achievement, and I highly recommend it for the best reason: You won't get removed from the session due to inactivity. Although you 'could' rubber band this, make a little bit faster as Online Players will do the games faster meaning progress should go quicker, you risk the game freezing or lagging out due to host disconnections meaning you will be kicked to the main menu. Those extra minutes you saved by playing Online has the risk of freezing making you waste hours if you plan to leave this overnight.
You want to do the following:
Offline With Bots
Any Map (Although Shoots has less areas to move around.)
Surprisingly this achievement could have been more heavy on tools to make this possible, but you don't even need a wired controller or a rubber band to keep moving. You won't get kicked for inactivity and your controller shutting off won't matter as the game will continue without you. Also, you will be getting these Awards towards your Awardist achievement. These awards are:
Shoots Vet (Win 5 Arms Race on Shoots)
Baggage Claimer (Win 5 Arms Race on Baggage)
Practice, Practice, Practice (Play 100 Games on Arms Race or Demolition)
Gun Collector (Play 500 Games on Arms Race or Demolition)
King of the Hill (Play 5000 Games on Arms Race or Demolition)
You can track the progress for this achievement on the pause menu. My Accomplishments > Awards > Arms Race & Demolition
These are for doing absolutely nothing but leaving your Xbox on whenever you're not going to use it. Although some people claim to have their Xbox Overheating, I personally have left it on 24/7 for weeks while boosting other games and it has never overheated. (I use the old Xbox model.) I just have it in a well ventilated area without a fan blowing on it and it's been fine. If you have it in a closed in area then I'd recommend moving it or having a fan beside it for safety.
I'm working on this and the games only take a few minutes for an Arms Race game to finish, compared to Demolition that it takes 11 rounds for a game to end plus restarts in rounds that take even longer. Of course, you can idle Demolition for the Map Wins Rewards if you want to get that out of the way as well. If you have any other tips that'd be great to make this fast for others.
Note: I left this overnight for 8 hours give or take, and it completed a total of around 100 Games. This achievement will take a while, so whenever you have something to do just leave the game running and it'll take care of it eventually. Be sure to grind the Arms Race games for the God of War to work on that tedious achievement as well.