What does the "monkey head" icon mean in the challenge mode menu?

Next to each difficulty in challenge mode, there are two icons that can be either unlit or lit.

It's obvious to me that the checkmark icon means you've completed a playthrough of the matching difficulty.

But what does the "monkey head" icon mean? I achieved it in my Casual and Expert playthroughs, but not my Master playthrough.

It seems to be related to the missions, as you can see in this screenshot I took from a youtuber:

Next to each mission you can see the "monkey token" that means the mission is achieved, every mission was completed, so Reverse Mode now has that monkey icon, too.