How can I get Xina's slipper?

Hint 1 of 11:

This is a pretty complicated puzzle.  There are several ways to work out the
logic, but you first might want to start by trying to get King Bodd to use
the slipper.

Hint 2 of 11:

Slippers are often used to kill bugs.

Hint 3 of 11:

So dig out a roach from the roach motel by having Fulbert crawl into it.

Hint 4 of 11:

The king's son Tibo might help you here if you gave him a new toy.

Hint 5 of 11:

Give him the gun that you took from the guard in Xina's chambers.

Hint 6 of 11:

Then look for something that Tibo might be able to use as a target.