Is the order of bosses fixed?

Technically, you can fight the bosses in any order that you want. There's nothing in the game that will prevent you from doing so. There's only a single boss room in each area, so you know who you'll be fighting before you try. ie. Khidir is always the Castle boss.

The generally accepted difficulty level is ordered as:

  • Castle
  • Forest
  • Tower
  • Dungeon

And the map in the first room supports that, as do the journal entries. If you're going for easiest to hardest, that's probably the best way to go about it.