I'm more familiar with the Northern Paiute tradition, but the two are close. The paúngaa’a, which translates as “water baby,” is a name that does not match the sinister quality of the creature. This ruler of the water plays an important role in a testimonial legend that tells of a woman who left her infant in a cradleboard by the water while she gathered edible plants. She hears her infant crying, and so she returns and attempts to suckle the baby. When the baby opens its mouth, it reveals huge fangs, and it bites into the breast of the woman. It is, in fact, the paúngaa’a, which has devoured the baby and is now chewing on the mother. The woman must quickly summon a shaman with paúngaa’a power to chant the demon away. The supernatural being responds by retreating back into the water. This legend warns about the dangers of the water and about not being an attentive mother. To achieve this, it calls on the belief in a ruler of the water.

Any affinity to the Northern European mermaid is only in a few shared characteristics: a human-like dweller of water. In other respects, the two traditions are far removed from one another.

For information on Shoshone traditions, I strongly recommend that you look at Volume 11 of the Smithsonian Handbook of North American Indians. It will give you the information that you need. It should be available through interlibrary loan at your local library.