Just to clear up some confusion...
UPDATE: Grunt kills do not count toward this achievement!
1. You need 10 headshot KILLS, not 10 headshots. The shot that kills the enemy must be a headshot.
2. The kills do NOT have to be consecutive (10 headshots in a row). Mine certainly weren't.
You can do this with any gun, not just the sniper. While I did this without, many folks are saying it must be done with the sniper or beam rifle. I don't know if this has changed, but sounds like it's easier to just go with that :)
4. You can do this in campaign or multiplayer.
Easy method #1: Start the campaign level "The Ark" at mission start on Normal. As you walk up the hill, there are several enemies waiting for you. Kill as many as you can with sniper headshots. If you don't have enough kills by the time all the enemies are dead, simply move to the next area where there are many more. You can take as long as you need and stretch this over the entire level if you like, but by this second checkpoint you probably will have the achievement. Just take your time and aim.
Easy method #2: Play Lone Wolves. You will probably unlock the achievement within a few games, if you can manage 10+ kills (really shouldn't be a problem).