What are the benefits of a non-orthogonal (scissor) tail-rotor?
(Source)
The comments and answers already say it's for noise reduction. What's more intriguing is the how:
The blades are not coplanar (image).
The tail-rotor of the Apache rotates clockwise (video) when viewed from the port side. The nearest blades (nearest plane) to the viewer are the leading blades of each group. A group is two close blades regardless of plane, e.g., 1 and 2 as labelled above are a group, 1 is leading.
The thrust of the tail-rotor is being directed away from the viewer (port to starboard), which means the viewer is looking at the pressure side of the rotor.
Below on the left is what it looks like from behind the Apache. This arrangement allows the trailing blades (2 and 4) to miss the wake from the ones ahead of- (and closest to-) them.
(Own work) Left: Apache; Right: coplanar normal spacing. View is from behind and thrust is left to right.
This L scissor configuration, as it is known, where the lower blade is leading yields more thrust due to the better interaction.


Based on extrapolation of the test results and calculations, the increase in thrust over a conventional four-bladed rotor of the same dimensions is about 10%. Rozhdestvensky attributes Bell's failure to come to similar conclusions to their use of a very small model.

And quieter, too
Noise measurements during flyovers were made with a Havoc having the four-bladed scissors tail rotor and the three-bladed tail rotor from the Hind. The two rotors made about the same noise at low speed but at high speed the scissors rotor was quieter. The primary reduction was in the &quot;broad-band&quot; frequency range from 600 Hz to 2000 Hz. Much of the noise at these frequencies is due to the effects of the tail rotor working in the confused wake of the main rotor. The scissors rotor apparently acts more like a two-bladed rotor in this situation.
(Helicopter Aerodynamics Volume II, p. 72.)