The solutions posted work great but I read another method that can save time and patience especially if you just beat the game on normal. I have used it for the hard and insane achievements and it only took 10-15 mins.
***Credit goes to x pelon x on x360a***
Found a new solution instead of playing all through the level.
After completed the game on Normal mode, go to the interface & just copy your save data on a USB Key.
Launch the last chapter/level choosing your difficulty (from your hard drive).
Quit the game and go to options game.
Select "stockage device" & USB Key.
Go back to campaign > Continue.
The last checkpoint will be loaded, you need to kill just 5/6 guys (not too hard if you have kept the sniper rifle) and finish the game for the achievements.
*Update from Eric Filtro* Perfect solution. To make it just a little bit clearer. Once you beat the game, copy the file to another device, let's say the USB. Now this is the important part. When you go to Select Chapter, first make sure you are loading from your Hard Drive by going to Options, Select Storage Device, Hard Drive. Now select chapter with the difficulty you want to play in. Once you start, quit and go back to Options, select the USB, and choose Continue campaign. I messed up at first because I didn't pick the Hard Drive the first time around and I actually overwrote the last checkpoint.
*Update 2 from Grizzly Bear*: With the addition of cloud storage, you can use a cloud saved game rather than a flash drive.
*Update 3: David1231231 has confirmed this still works Oct 2018. Added that if you quit the game right after the achievement pops the game does not overwrite your save file so you can use it to load for the other difficulty.
**Note: According to Vito084 this works for the FRE/GER version as well.
If you have any questions about the above method just leave a comment and I'll help you out as much as I can. Enjoy!