This achievement isn't too bad if you are going for the other Eliminator achievements. A lot of Eliminator is luck based so don't get too frustrated over certain matches.
To initiate a Head-to-Head, you have to honk your horn close enough to another player. You won't know where you are racing too until after a couple of seconds. I would suggest leaving you audio on because your GPS will say "Turn around when possible" prior to your map updating if you are heading in the wrong direction.