So in summary, in order to fight and kill psychic shriekers, they will have to find a way to enter the spiritual dimension, search for the psychic shriekers in the spiritual dimension, survive in the spiritual dimension long enough to find them, and finally somehow separate a psychic shrieker from the herd to fight and kill it or take on the whole group of psychic shriekers at once.
Of course, one will have to do all of these and be able to return safely to the physical dimension, or everything they accomplished in the spiritual dimension wouldn't count. If they are not careful, they might just die in the spiritual dimension.
There are clearly a lot of problems with meeting this advancement requirement, most of which come from the environment. The danger of the spiritual dimension accounts for at least 50% of the difficulty of the advancement requirement.