So, this will probably be a 'no shit' kind of thing to mention, but it's helped a few guildies now get it, so I hope it helps you too.
This is most effective when you BG late eve/early morning on your server, as you're more likely to come across less 'real' players. This is also easiest for stealth characters to pull off with little to no interference.
My preferred battleground for this is Arathi Basin due to a fixed respawn location which is out of the way of others, but the same principle applies to them all. You'll notice later in the eve, their are far more people using bots/AFK dodgers, and you can use that to your advantage. Make your way on the outside of the map (follow the largest wave of your own allies to prevent risk of dying) and try and stay out of sight. Mosre likely then not, you'll see an Opponent sitting at the enemy spawn point - kill them, duck around the 'house' structure to avoid others spotting you, and wait for the respawn wave. Easy breezy.
I know it's pretty common sense, but it's effective for those having issues getting the achievement and I thought I would share. G/L all!