I go to resume game and the initializing mission screen pops up and it says press a to enter game.

So I press A and all I get is a black screen and it crashes and I have to turn off and restart my 360 to be able to do anything.

I heard you can get back to the mission by going into the replay mission menu and restarting it from there but if youi do that does it cause you to miss out on the achievement for finishing the game?

It happened when I was loading the checkpoint for the first time after dying aswell by the way.

Replaying a mission won't disable the achievement unlock, you don't have to beat the game on one save play through when looking at missions on the replay screen it tells you if you have beaten the mission on which difficulty.

If you don't want to to restart the mission completely try clearing your system cache (this may or may not work)
if that doesn't work restarting the mission is the best possible solution.

Yeah, what he said. This happened on the second mission on supersoldier. When I went ot replay mission everything worked fine.

Thanks good to know.
I first cleared my cache and then it wouldn't allow me to download the update for the game.
I cleared the system cache again then it allowed me to download the update.
The clear cache didn't bring back the mission so I restarted the mission and everything is grand now.
Framerate seems a bit smoother aswell I think after the clearing of the cache.