How do I get the "Payback" achievement?

The proper way to get the achievement, is by using an object to shield yourself from the Hunter's flechettes, then using the stuck flechettes to kill the Hunter.

This is demonstrated in this video:

Throwing would have worked too, as shown in this next video (the quality is much lower and you can skip to 3:30)

When throwing, it is advised to use objects that have a low chance of killing Hunters when thrown. Using a barrel or tire is recommended over a radiator, for instance.

It's the explosion of his own flechettes that must kill him so when you threw something at his face and got the achievement, it was because there were flechettes stuck to the object.

The easiest way to achieve it is to take a barrel with the gravity gun, wait for the hunter to attack you with flechettes, then run toward him with the barrel and wait for the flechettes to explode near him. Notice 2 things, you can get this achievement while you are dead (when the screen goes all red), you can hurt the hunter before with the shotgun and just finish him with his flechettes and still get the achievement.