Ichthyology is best characterised as Science. None of the other field of studies apply to Ichthyology.
Pseudoscience are beliefs or theories that have been considered scientific. However, they are disapproved scientifically because lack of facts and evidence.
Cryptozoology is study of animals that are rumoured to exist. (Bigfoot, Loch Ness Monster, etc) It is connected with pseudoscience.
Mythology can refer to myths or the study of myths.
As you can see, the study of fish does not apply to any of the area of studies except for Science. Ichthyology applies to Science, because it is a scientific study is different aspects of various species of fish. This includes history, behaviour, and growth.
