Guardians are enemies that Cerberus will throw at you in both single- and multiplayer. They are identified by the large shields they will hold in front of them to guard themselves from damage... in theory.
You will need to land ten fatal headshots on Guardians through the 'mail slot' (the little slit toward the top of their shields that they use to see through), while the Guardians have their shields lowered and are (most likely) advancing toward you. It is possible to knock them off-balance, so if you see them stagger a bit and wave their shield wildly your headshot will not count. These can be accomplished in singleplayer, multiplayer, or any combination of the two.
Only Sniper Rifles are really effective at this. Even powerful single-shot weapons the Mattock aren't going to cut it unless they're heavily upgraded and modified, but at that point in the game you'll probably have the achievement already anyway. I recommend using the Valiant since its three-shot clips allow you to get more than one shot in if you're using an ability like Adrenaline Burst. Additionally, for anyone who can lower the difficulty (aka, not an Insanity run) to Casual will find a ridiculous aim assist will allow you to perform headshots with methodical frequency. Feel free to make use of it.
It is also of note that a frontal headshot through the slit isn't always necessary. Not that it's a difficult achievement to get anyway, but at least two of my kills were headshots achieved through the side, when the Guardians were pursuing my squadmates. Xaero Hour has also confirmed that this is possible to gain progress for with a side-shot headshot. This may help you if you're playing on a higher difficulty and don't want to face them head-on yourself, although the exact angle or specifications that make it no longer count toward this are still unknown.