About time. For those not in the know, Call of Duty: Classic, the original CoD, is going to be released alongside Modern Warfare 2 as a "timed exclusive" for those who buy the Hardened or Prestige editions of the game. No release date for XBLA/PSN has been announced, but it's sometime afterward for roughly $15 real dollars. Expect these to be the PSN's Trophies, as well.
The achievements, gathered by my favorite achievement-tracking site, xbox360achievents.org, has compiled the list comprising of 12 achievements. There is your standard fare of achievements, such as normal story progression and actually beating the game. However, there are some oddballs such as beating a mission without dying or loading a checkpoint and beating a mission using solely your pistol (melee's do not count).
Source • X360A - Call of Duty Classic Achievements