This is the layout of the palace. It doesn't appear to be randomized in among different seeds, so this should just be "it" unless the devs patch the game.

You will end up going more-or-less all over it clearing out enemies. They won't respawn unless you leave the palace entirely (or go fight the bosses... but by then you've solved the puzzle).

You will need to kill all the enemies on the lower left portion of the map to get the lower-left door to open. This includes the spiders that just have their shadows showing.

The red arrows are just to show the wrap-around nature of the map and don't show a particular route.