Demon Adi was the son of Andhaka. It was Shiva who had put an end to the tyranny of Andhaka by killing the demon. To avenge his father’s death, Adi offered prayers to Brahma. He performed intense austerities and did penance to please Brahma. Finally, Brahma relented and gave him the boon that he will only die if left his present form and took another form.
Demon Adi after receiving the boon thought of plans to enter Kailasa, the abode of Shiva. He did not want to fight the Shiva Ganas and alert Shiva about his presence.
He also knew that he did not have the power to over come Virabhadra, the main Shiva Gana.
To avoid being sighted, Adi was forced to take the form of snake to slip into Kailasa without the Ganas noticing.
Then Adi took the form of Goddess Parvati and went near Shiva. But Shiva immediately realized the demon in disguise and overpowered and killed him.
This story is mentioned in the Padma Purana and Matsya Purana.