Pratyangira

Prathyangira (Sanskrit: प्रत्यङ्गिरा, Tamil: பிரத்யங்கிரா; "Prathyaṅgirā"), also called Atharvana Bhadrakali, Narasimhi and Simhamukha Lakshmi is a Hindu Goddess associated with Shakti. Prathyangira is the incarnation of Goddess Lakshmi and the divine energy of Lord Narasimha, an incarnation of Lord Vishnu. Prathyangira is described as a powerful goddess with a male lion’s face. She has a female human body representing the union of Lord Vishnu and Lakshmi. This combination of lion and human forms represents the balance of good and evil. In Shaktism, Pratyangira is Siddhilakshmi, a form of Guhya Kali. In Durga tradition, Pratyangira is Purna Chandi, the fiery destructive power of Brahman. In the Vedas, Pratyangira is Atharvana Bhadrakali, the goddess of Atharva Veda and magical spells.
Legends.
There are many "Hindu" texts that state different legends of Lord Narasimhi. 
According to many "Puranas", Narasimhi with the face of a lion, fierce claws and four arms is the "Shakti" of Lord Narasimha. Goddess Lakshmi took the form of Narasimhi in order to pacify the ferocious Narashima. At the end of Krita yuga, a glittering spark appeared from the universe and transformed into a wicked demon named Vipulaasura. Vipulaasura disturbed a group of 8 sages who were performing rituals of Goddess Lakshmi. This angered Goddess Lakshmi who transformed a holy lotus flower into a "kavasa" or a strong shield. It is also mentioned that the lotus which was transformed had 562 petals in it. The shield provided a great protection to the 8 sages, allowing them to perform the holy rituals without any disturbance. After that, Lakshmi took the form of Narasimhi and defeated the demon Vipulaasura. 
According to the "Markandeya Purana," "Shiva Purana", "Vathistabhaana Purana (AD 13)" and the "Vimathgira Purana", in the beginning of the Treta yuga, the Lord Narasimha, an avatar of Vishnu, killed the unruly King Hiranyakashipu by tearing up his body and drinking his blood. Because of the anger in Hiranyakashipu's body and blood Lord Narsimha drunk on rage and could not be stopped. To calm him down, Lord Shiva came down as Sharabha, a bird-animal-human hybrid. Upon seeing this, Lord Narasimha transformed into Gandaberunda, a two headed bird to fight against Sarabheswara. These two beings fought a long time terrorising the world without reaching a solution. Later, Lord Varaha, the boar incarnation of Vishnu appeared and helped Narasimha to fight against Sarabheswara. Seeing this Goddess Parvati took the form of Shoolini devi and appeared beside Sarabha. All the Devas or Demigods went to Vaikuntha and requested Lakshmi to pacify Narasimha's anger. Lakshmi then took the form of Pratyangira and finally, along with Prahlada, pacified Narasimha. Bhu devi in the form of Varahi pacified Varaha and each deity returned to their abode.
In another version in ancient times when two Rishis, Prathiyangira and Angiras, were meditating they re-discovered a Goddess through a Moola Mantra who was nameless. Later She privileged the rishis by naming Herself after them and hence She was called as Prathyangira Devi. Narasimhi is another name of Hers. 'Nara' means human and 'Simha' means lion, so she got named thus as She appears with a lion's face and a human body. 
The term "Prati" means reverse and "Angiras" means attacking. Thus, devi Pratyangira is the one who reverses any black magic attacks. In temples of south India, She is also eulogized as Atharvana Bhadrakali as the She is considered the ruling Goddess of the Atharva Veda, the scripture which contains spells to conjure and cure.
Pratyangira is one of the chief warrior goddess of Lalita Tripura Sundari's army called Shakti Sena. Adi Parasakthi at an earlier time during the war between her and Bhandasura gave two boons to Pratyangira that the protection offered by Pratyangira is invincible and no deity can overcome it. Also when invoked for offensive purposes Pratyangira give invincibility and sure victory to her devotee. Thus Pratyangira is a very popular deity among the Kshatriyas warrior caste. She is often described as the ultimate Goddess to be worshipped for defensive and offensive power.
Association.
In some images she is shown as dark-complexioned, terrible in aspect, having a lion's face with reddened eyes and riding a lion or wearing black garments, she wears a garland of human skulls; her hair stands on end, and she holds a trident, a serpent in the form of a noose, a hand-drum and a skull in her four hands. She is associated with Sharabha and she has a variant form, Atharvana-Bhadra-Kali. She is considered to be a powerful repellent of the influences generated by witchcraft and is said to have the power to punish anyone doing Adharma. It is said that when Narashimhika shakes her Lion's Mane, she throws the stars into disarray.
In Hindu Epics.
Prathyangira is also mentioned in the Hindu epic "Ramayana". Indrajit was performing "Nikumbala yaga" (a sacred ritual to worship Prathyangira) while Rama and his soldiers were waging war in Lanka. Hanuman came down to stop this ritual because he knew that if Indrajit completed it, he would become invincible.
Worship.
Tantra classifies deities as Shanta (calm), Ugra (wrathful), Prachanda (horrifying), Ghora (terrifying) and Teevra (ferocious). Pratyangira is considered as a . Pratyangira worship is strictly prohibited for people who have namesake Bhakti. Pratyangira worship is only done by the guidance of a Guru who is proficient in Tantra.
Worships dedicated to Pratyangira is performed at many places for the welfare of the people and for eliminating the influences of evil forces. In some temples Pratyangira Devi Homam (Havan) is performed on days of Amavasya.
Eight kinds of Tantric acts.
Like all Tantric deities, she can be invoked for the eight kinds of acts usually performed. They are appealing, growth, increasing, attracting, subduing, dissention repealing and killing. Detailed information is found as to what kind of materials are to be used for the respective aim, and the number of recitations to be performed. It is further said that any act performed invoking this deity, especially the bad ones like killing and subduing, it is impossible to retract it even when the doer wishes.