What was there to be blamed in thee, O Viṣṇu, when thou declaredst, I am Sipivista? Hide not this form from us, nor keep it secret, since thou didst wear another shape in battle.
Sipivista means either bald or infused with the sun's rays, but my question is, what is the form being referred to when it says "another shape", and what battle is it referring to? I think I have an answer to the second question; this verse recurs in Book 8 Chapter 1 Hymn 4 of the Sama Veda, and Sayana's commentary for that hymn says this:
Vishnu formerly abandoned his own form, and assuming another artificial shape, succourred Vasishtha in battle. Recognizing the god, the Rishi addresses him with the verse.
There's only one battle Vasishta is known for - the famous Battle of Ten Kings (AKA the Dasarajna), where the Bharata king Sudas defeated a powerful alliance of many kings. The Bharatas were successful in taking over India, which is why we call India Bharata-Varsha today. In any case, Vasishtha, who was Sudas' guru at the time, was instrumental in his victory, because he was able to get the gods, particularly Indra and Varuna, to participate in the battle on the side of Sudas.
So it looks like Vasishta got the assistance of Vishnu as well, which wouldn't be surprising as Vishnu and Indra are often closely associated (since Vishnu's incarnation Vamana is Indra's little brother). So the question remains, what's the alternate form that Vishnu assumed in the Battle of Ten Kings? Are there any other scriptures that describe Vishnu's role in this battle?