343 Industries has announced that the studio will be closing servers, and sunsetting services for several Xbox 360 Halo titles next year. Halo: Reach, Halo 4, Halo 3, Halo 3: ODST, Halo: Combat Evolved Anniversary, Halo: Spartan Assault (Xbox 360), and Halo Wars will all have their services either reduced or disabled next year in December 2021. This gives you a year's warning to grab any achievements from the affected games before they become discontinued.
According to 343 Industries, achievement support will "vary by title as any that specifically require matchmaking and challenges will no longer be obtainable." The culprits that will lose achievement support are Halo: Reach, Halo 4 and Halo 3. The chart above notes that achievements for Halo 3: ODST, Halo Wars, and Halo: Spartan Assault should remain unaffected, while Halo: Combat Evolved Anniversary's achievements can be all unlocked offline. To be on the safe side, it'll be worth working through all Xbox 360 online-flagged Halo achievements just in case.
All of these games have also been delisted from the Microsoft Store, so if you haven't played these titles and want to start working your way through their achievement lists, you're going to need to find physical copies of each game. As a side note, Halo: Spartan Assault (Xbox 360) does have one partly discontinued/unobtainable achievement and is not available physically.
343 Industries says that online services will be shut off sometime after December 18th, 2021. You have a year to unlock any of the achievements from these games before they become discontinued.
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