How to get rid of pigeons under an air conditioner outdoor unit, on the high floor of an apartment?
If they have a nest with eggs or chicks, you will pretty much need to remove the nest to get rid of them because they will be very persistent in protecting the nest.  If you don't care about being humane, you could make an "L" shaped tool to reach under the unit and knock the nest out.  Use a mirror on a long pole to see what you're doing.

If they are just congregating under the unit, you can use repellent foil.  It's a Mylar ribbon imprinted with an irridescent holographic pattern.  You can find it at places like Amazon or big hardware chains.  Here's an example:



The patterns vary.  Apparently, birds can't focus on the pattern and it scares them away from landing.  Just hanging it in the vicinity keeps birds away:

  

In the picture above, there is some hung vertically and some horizontally to protect different areas.  In the picture below, they just have some ribbons of it that flap in the wind:



For your problem under the unit, you would make a big loop of it, drop the loop under the unit from the window (assuming it's under a window), and fasten the ends in a reachable spot.  If there is nothing good to fasten them to, and you can reach the top of the unit, staple the ends to a board that sits on top of the unit.  You might want several loops of different lengths if there's a big area underneath.  If you use a board, secure the board with adhesive, or double-sided mounting tape, so wind doesn't blow it off and cause damage or injury below.