343 Industries has actually announced that the studio will be closing servers, and sunsetting services for numerous 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 decreased or disabled next year in December 2021. This gives you a years alerting to grab any achievements from the affected games before they end up being stopped.
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 ought to stay untouched, while Halo: Combat Evolved Anniversarys achievements can be all unlocked offline.
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As a side note, Halo: Spartan Assault (Xbox 360) does have one partly discontinued/unobtainable accomplishment and is not offered physically. You have a year to open any of the accomplishments from these video games before they become stopped.