there are no spells that can physically turn you into a mermaid. this has been said many times, because it's true, real spiritual magick is not like the magic you would see in movies and tv. the spells cast in Harry Potter and Charmed are fantasy, used to entertain. the spells cast in real life utilize natural energy to create subtle changes to help us in life. it is found in nature, it is a part of nature, and it cannot go against nature. humans do not have the ability to grow wings and fly, turn invisible, levitate, or grow a tail and breath under water. i know it sucks to find this out [sorry if i made you mad] but it's the truth.
now, i have been told mermaids are real on the astral [sort of like spiritual energy] i know of people who call upon other astral beings [such as demons, dragons, faeries, and vampires] to aid in their spell casting, you could try incorporating their energy into your rituals. i don't know how well this would work as i don't deal with mermaids [have barely studied them] but it's an option. keep in mind you cannot physically change into any other being, you are human, and nothing [short of surgery] will change this fact.