A couple of the DLC Achievements specify doing it all in 1 game, but most of the ones where you have to do something multiple times (like 20 Mantis stomp kills) just say "In X DLC Matchmaking, do whatever x times. So I'm assuming those just keep track and you can do it over multiple games, correct?
Also, has there been any indication from 343 that the Castle DLC playlist will just turn into a DLC playlist? I missed out on the Crimson and Majestic DLC playlists and those maps barely ever come up now for me, so it will be insanely hard to get those achievements.
1. The 20 Stomp Mantis kills and the mounted turret achievements can be done in multiple playthroughs. Unless of course, you are godly with both mantis stomping and turret killing in a single game.
2. To my knowledge, 343 has not announced anything making a DLC playlist only.
3. If you are missing any Majestic/Crimson achievements you better hope everyone in the lobby has those map packs and votes on them or make friends online with people who have them as it will be more likely they show up in the regular playlists. I.e. Crimson = BTB, Majestic = IS, Team Objective, Extraction, Doubles.