Process of elimination can work well on some levels. Those with five or six hands will only be able to go in one or two spaces, and they'll need surrounding with friends.
Similarly, there are spaces where it's obvious the ghostly Whisprins or the lonely Poeglins can't go. Often, you'll need to tuck these away in corners, so start from there and the solution should come more quickly.
Sometimes, you'll end up with what looks like the correct arrangement, yet you're left with two or three unhappy monsters. Try tapping them so they link hands with others, and you'll occasionally solve the puzzle.