According to 343 Industries, the support of the achievement “will be different from the title which specifically requires matchmaking and the challenges will no longer be attainable.” The culprit who lost the achievement support is Halo: Reach, Halo 4 and Halo 3. Above the notes are the charts that are achievements for Halo 3: ODST, Halo Wars and Halo: Spartan Assault should remain unaffected, while Halo: Combat Evolved Anniversary Achievements are all offline. To be on the safe side, it would be worth working through all the Xbox 360 online-flagged Halo achievements just in case.
All of these games have also been removed from the Microsoft Store, so if you haven’t played these titles and want to start working through your achievement lists, you’ll need to find physical copies of each game. As a side note, Halo: Spartan Assault (Xbox 360) has a partially closed / unattainable feat and is not physically available.
343 Industries states that online services will stop for some time after December 18, 2021. It will be a year before you unlock any achievement from these games.
Thanks to everyone who sent this as a news tip.