You should first look for any of the pieces that are required to be in a specific place and place them. Next check to see if any of the remaining figures have a relationship with the figures already placed. If more than one. First look at pieces that must be on an end.if more than one piece remains, then analyze the relationship between the two, if any, and try to place with respect to those rules as well. Review the rules of any remaining pieces. Try to fit them in without violating the rules for the existing pieces.

When one piece have two places they can goes to, you can already place it in one of the two places, and keep in mind both possibilities. If that start to be too complex, just commit on one of the two, try to finish the puzzle, and if you don't manage to, try the other place.

At the same time look at hint which reduces a lot the options. Per example if there is 4 monsters in the same floor, then with 6 differents monsters that reduces a lot the options.

And there is an high chance to have any hint you take to be useful to find the solution. That mean that if the clues said that a bird can't be in position 3, then it's likely that this bird would finish in position 2 or 4. If that wasn't the case, it's likely for that hint to be useless to find the solution.