This is only partially true. Halo 2 for vista is not entirely shut down and still connects to xbox live. The only thing that does not work is the multiplayer function but you can absolutely connect your gamertag to it, play the campaign, custom games and unlock all the achievements. Yes even the multiplayer achievements can be unlocked still, this works because in halo 2 for PC you could always unlock multiplayer achievements in custom games so even though the multiplayer servers are down you can still get the achievements by playing the custom games with yourself since GFWL still connects to xbox! =D Let me know if you have any questions and you can see by my gamertag that I am a halo achievement hunter (have every achievement for every halo game across all versions). lol Happy hunting!
*for the overkill achievement you will have to kill your three guests and wait for one to respond before killing the next which was the hardest for me but on a small map with a bit of luck you can do it! =)
This video gives an exact guide for the multiplayer ones: https://www.youtube.com/watch?v=8HkR4YEw7oM