Does anybody have a similar light covering to this? I have tried pulling all the arms outward, pressing the arms up, looking for screws on the arms, and just sliding it out with a little bit of force. All no goes so far 
Lighting – How to remove light cover
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It looks like it just pulls down, there are usually little springs that keep it in place. Like the one pictured below
I had a very similar light, and the key was this:
Any upward pressure exerted from grabbing the glass created friction that made it not turn.
You want to touch as lightly as you can, near the edges, and try to apply rotational energy only, with no pushing up.
Unfortunately, that is roughly impossible to do if you're reaching so high that you need to press up on the glass to maintain balance. So, you still need to solve the problem of getting higher (and you should NOT climb on anything placed on a bed unless it's highly stable). But if you can get a bit closer, try less pressure, rather than more.
It feels very counter intuitive, but it helped me in a similar circumstance.
One other thing that may help, suggested by none other than @Joel Spolsky, was to try using rubber or latex gloves to allow you to produce more friction without more pressure.
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Best Answer
We just figured out how to change this. There is 1 arm that has a bunch of give, the other 3 are pretty static. It was a 2 person job... One pushes the whole glass part up to the ceiling, while the other 'bends' the one arm up which will allow the glass to come out.