One of the most famous stories of Vishnu is the Gajendra Moksham episode, described the Eighth Skanda of the Srimad Bhagavatam. For those who don't know, once a king named Indradyumna, who was a great devotee of Vishnu, was cursed to be born as an elephant named Gajendra. Gajendra's leg was once caught by a crocodile (originally a Gandharva king Huhu but was suffering under a similar curse). So Gajendra, remembering the greatness of Vishnu from his time as a human, started praying to him for help. So Vishnu came riding on Garuda, killing the crocodile with his Sudarshana Chakra and granting Moksha to his elephant devotee Gajendra.
But my question isn't about the story of Gajendra, but rather about the one who saved him. Strictly speaking, it was not Vishnu himself who saved Gajendra, but rather Vishnu's incarnation Hari, as described in the Srimad Bhagavatam:
O King, in the Tāmasa manvantara the sons of Vidhṛti, who were known as the Vaidhṛtis, also became demigods. Since in course of time the Vedic authority was lost, these demigods, by their own powers, protected the Vedic authority. Also in this manvantara, the Supreme Lord, Viṣṇu, took birth from the womb of Hariṇī, the wife of Harimedhā, and He was known as Hari. Hari saved His devotee Gajendra, the King of the elephants, from the mouth of a crocodile.
So my question is, what is the story of Vishnu's incarnation Hari? First of all, who are Harimedha and Harini? And what else happened in his life besides rescuing Gajendra?
We know that Hari rode on Vishnu's bird Garuda, although that's not so unusual since Krishna also rode Garuda, as I discuss in this question. (Rama didn't ride Garuda, but he did meet him; see my answer here.)
Another piece of information is that Hari apparently had the ability to travel to Vishnu's abode of Vaikuntha; the Srimad Bhagavatam describes him taking Gajendra. But do we know anything else about him?
Note that this Hari is different from Vishnu's other incarnation Hari, brother of Vishnu's incarnations Nara and Narayana, whom I discuss in this question.