What are the bosses and when do they appear?

There are multiple references to "bosses" in the developer's design notes.

I started with the enemy spawns divided into fairly explicit "waves", like maybe four would come at once then a break, then two at a time with shorter breaks between, then one boss, that kind of thing.

https://mightyvision.blogspot.com/2016/06/imbroglio-notes-3-monsters.html

The 16/16 endboss worked pretty well

It seemed good to get some kind of reward for killing a boss

Both bosses had this effect for a while

https://mightyvision.blogspot.com/2016/11/imbroglio-notes-11-spoiler-warning.html

What are these bosses and when do they appear? Do they have a small % chance to appear at any time or are they triggered by a gem level?

For that matter, is the Minotaur a boss or a mid/mini-boss? I think I saw one appear at like 55 gems, which doesn't seem to line up with the developer's goal of making things happen at multiples of 4.