Harvesters are the giant flying horse type enemies. You'll only encounter about a half dozen or so throughout the campaign. Use ammo and powers that are effective against armor for best results. You'll first start seeing them on Tuchanka. Specifically, you will be after one on that planet trying to save a team of Turians. Don't worry if you don't kill them right away, as it can fly off. The end of the mission mentioned specifically makes you kill it at the end. When fighting it, just make sure there is something in the way and you can shoot one of it's body parts that are exposed.
They were originally supposed to be an enemy in the first game that you could only kill in the Mako, and then were added in the second game with the intention of being an enemy you could fight on foot (http://www.youtube.com/watch?v=eeaTevItJ8U). It's looking like now, we'll finally be able to fight one (albeit a husk?). You got to see them in the second game in regular gameplay, but never got to fight or kill any.
On the mission on Tuchanka where you go searching for the Turian platoon there's one flying around just unload into it, The Harvester will fly away a few times but eventually he will stay still so you can kill it
It would be pretty damn hard to miss though, you see more than 5 different Harvesters during Tuchanka: Turian Platoon and can kill every one. The first one I saw flew off with one bar of armor left so I was worried I may not get another chance but got the achievement and killed plenty extra very quickly.
When on your way to save Lieutenant Victus you'll come up to a bit that seems to have an unending amount of enemies (Cannibals, Marauders and a single Brute) after killing off a few a Harvester will land to the right of where you entered the area. If you make your way towards it, you'll see a Reaper Blaster on a chest-high wall. Pick it up, aim at the harvester, charge it's shot and boom. Achievement unlocked.