How do bats move?
Is there a pattern for which direction a bat enemy will move, and if so what is it? Or is it just a random walk?
I've gathered that bats only move during every other beat, but there doesn't seem to be any pattern on which direction they will move to. Especially with the boss versions, this makes them hard to kill with a dagger without taking any damage, where you have to spend the turn they don't move to get adjacent to them.
Bats move in a random direction. There's no predicting it.
Blue bats are restricted to up/down/left/right movement. They move every two beats, but it might be on either odd or even beats. This means that rooms full of bats are more dangerous than you might think, because they're all moving at random, and not all on the same beat.
Red bats are restricted to up/down/left/right movement. They move on every beat. This means that they will always move to a tile of the same color. When tangling with them, be sure you're not on their color, keep moving, and you will be safe.
Green bats move in any direction, including diagonally. They move on every beat.
Black bats are similar to red bats, in that they are restricted to up/down/left/right movement and will move on every beat. However, black bats will always attack you if you move into a (non-diagonal) adjacent space. This means you can't just move next to a black bat and hope it doesn't pick your tile to randomly move to.
According to the wiki, yeah, they just move randomly every other beat. I found that info here, if you're interested in reading about more of the monsters.