I don't recommend trying for this achievement on Ironman. You'll probably want to make a save before you begin, so after you unlock the achievement, you can go back to where you were and finish your campaign the way you wanted to.
Wait until you have a captain and can buy the Squad Size II upgrade. By this time, you will also have a decent amount of stats, abilities, weapons upgrades, etc., all of which will help. I don't think you need to worry too much about bringing a certain weapon, mod, squad member, etc. It's more about having a fullly equipped midgame-level squad you're comfortable with than about having a specific trick up your sleeve.
Next, wait until you have a mission with The Horde sitrep. (This means the map has only Lost; no Advent or aliens that you have to fight simultaneously.) You may see this sitrep on one of your guerilla op choices when you actually wanted to choose a different mission. No problem, that's why you're making a save, remember? After you've saved, change your difficulty to Rookie, select and load out your squad, and begin the mission. Once the mission is started, you may want to make another save that you can scum in case you don't get your 15 headshots on the first try.
What I did was send my soldiers out in two groups of three to find the Lost pods. Once I found them, I didn't shoot any Lost, I just dashed my soldiers towards a center point where they could all get on high ground. This map had an Advent train on it, which worked out well as a shooting platform. Since I was running without making any attacks, some of the Lost got within melee range and attacked my soldiers with their little sissy slaps, which is fine because close range just makes them easier to kill. When I began making headshots, all of my soldiers were more or less together, and there were about 20 Lost surrounding them on all sides.
I used my Templar and my sharpshooter first, because their autopistol and pistol have infinite ammo without reloading. It helps a lot to start off getting 7 headshots without using any actions or ammo.
You'll want to be aware of your weapon's minimum damage and the target's hit percentage. It's often better to go for a lower hit percentage on a lower-HP target than a 100% hit chance on an enemy that might not score a headshot. For example, if your sharpshooter's pistol has a damage range of 3-4, and your choices are one target with 4 HP and 100% to hit, and another with 3 HP and 95% to hit, I would go for the 95%.
This clip is from my game where I got the 15 headshots and unlocked the achievement, although the Game DVR doesn't include the achievement popup. As you'll see, when I got my 15th headshot, I had three soldiers who still had both actions left, and I never use auto-loaders, so the moral is, this is very doable and you don't have to bend over backwards trying to set up the perfect tactical situation.