According to tāntric lore, Mahiṣāsura first took birth in Raṃbhakalpa as the son of Raṃbhāsura. In that birth, he was slain by Parāmbā in her form as Aṣṭādaśabhujā Ugracaṇḍā who used a śvetakhaḍga to kill the demon. This form of Parāmbā is invoked through the famous Navākṣarī mantra.
Again, in the Nīlalohita kalpa, Mahiṣāsura took birth and this time, he was killed by ṣodaśabhujā Bhadrakālī who used a śvetabāṇa to destroy him.
Finally, he was born a third time in śvetavarāha kalpa but he remembered his previous births by the grace of sage Jaigīṣavya. Having realized the possibility of death again at the hands of Mahāmāyā , he resorted to ekānta bhakti (kāyika, vācika, mānasika) and immersed himself in the upāsanā of Parāśakti. After twelve-thousand years of upāsanā, Bhagavatī manifested before him and he addressed her thus:
“O Great Goddess! Having assumed highly ferocious and astonishing forms, you have slain me twice before. Pray tell me which terrifying form you plan to assume this time to kill me and relieve the devas of my fear?”
The Supreme Goddess said, “O demon, how is knowing that going to be of any use to you? It will only induce greater fear in you. If you insist, here is one of my forms”. Having said so, Parāmbā assumed the terrifying form of Ugracaṇḍā sporting eighteen hands. Flames emanated from her mouth and she held various astra and śastra in her lotus hands. She wore a muṇḍamālā and made terrible noises of hūṅkāra. Unable to bear the fury of her form, the demon closed his eyes and folded his hands in surrender.
Parāmbā now assumed the ferocious form of Bhadrakālī sporting sixteen hands. Again, the asura was greatly petrified and sought refuge at the feet of the Great Goddess. When she assumed her svābhāva sundara svarūpa once again, Mahiṣa sought from her three boons. He requested her to kill him, if at all she had to, in a gentle form (saumya svarūpa). As a second boon, he requested Mother to place her foot on his head to hold his face in position so as to allow him to focus on the lotus face of bhagavatī till the last shred of prāṇa remained in him. Thirdly, he sought yajnabhāga for himself, like the devas. Thus, Parāśakti assumed the supremely beautiful form of daśabhujā Kātyāyanī to kill Mahiṣāsura for the third and the final time.
So, Ugracaṇḍā, Bhadrakālī and Kātyāyanī are three important forms of Durgā worshiped in śrīkrama tantra using nine, twenty-one and eleven lettered mantras respectively. During śarannāvarātrotsava, all three goddesses can be worshiped, or one of them.