The Lord appeared as Nara and Narayana in Badrikasrama. Pillai Lokacharya, in his Mumukshuppadi, gives the reason for this avatara, said P.T. Seshadri in a discourse. Samasaris do not know about the Lord. They do not know why they have been born. They do not know what kainkarya they have to do for the Lord. Samsaris are like a man who has lost something, but does not even know what he has lost. The Lord did not want them to continue to suffer in samsara. So, He came as Nara Narayana, did penance in Badrikasrama and gave us the Ashtakshara mantra.
Thirumangai Azhvar also records this in his Peria Thirumozhi. While Narayana was the Acharya, Nara was the sishya. While it is understandable that the lord should have come as an Acharya, why did He have to come as a sishya as well? Pillai Lokacharya answers this question also. He explains that we do not know how to be model disciples. To show us how a sishya should behave, He came as a sishya too. So, in his very first avatara as Nara Narayana, He shows the world how to be an ideal Acharya and an ideal sishya. In His next avatara, He came as a swan, to save the Vedas. This was followed by the Dattatreya avatara, Sanatkumara avatara and Rishabadeva avatara. These four were amsa avataras, that is partial incarnations.
Then comes the Hayagreeva avatara, says Dhrumila, one of the nava yogiswaras. In this avatara, the Lord killed Madhu and Kaitapa and retrieved the Vedas, which had been stolen. Then came the Matsya avatara. In this avatara, He asked king Satyavrata to protect all life forms during the deluge. Dhrumila also talks of the avatara He took to save Gajendra, the elephant. Dhrumila tells king Nimi that the Lord will soon be born as Krishna.
