My steps listed below.
1. Installed Crysis 2 to harddrive
2. Launched title and advanced through title select screen
3. Selected Campaign and New Campaign
4. Selected Supersoldier difficulty
5a. Played through the game in 3 sittings
5b. Never once was a level restarted.
5c. Only the option "Resume" was used when returning to campaign.
5d. Difficulty was never changed. The only setting adjusted was subtitles.
5e. Campaign was started before ever entering an online match.
With those steps I wasn't able to unlock the Supersoldier achievement though I have all the special videos that unlock when completing the game on that difficulty. All other campaign achievements triggered correctly on my first play-through. Many users believe this to be related to "replay mission," however I have not touched that option as of yet. Some users suggest starting the game immediately in Supersoldier causes various achievements to not trigger properly. It is advisable to start a play through on Soldier, then exit it to begin your new Supersoldier play-through.