Do Xbox 360 Achievements Disappear If You Unplug the Console?
No. Achievements are tied to your Xbox Live profile (Gamertag) and stored on Microsoft's cloud servers—not the console's hard drive.
What Unplugging Actually Affects
Unsaved Game Progress: If you yank power mid-game without saving, that session's progress (level completion, items found, stats) is lost. The save file on the HDD/USB may corrupt.
Local Cache: Temporary files, marketplace data, title updates—rebuilt on next boot.
What Stays Safe
Achievements / Gamerscore: Synced to cloud at unlock (requires momentary connection). If offline, they queue and sync next sign-in.