[Query] Which purana describes the story of buddha's battle with maa durga?
No purANa describes such a story. Some Buddhist Tantras (especially the yoginI tantras) have borrowed wholeheartedly from Hindu Tantras. Similarly, the medieval, so-called Hindu Tantras have borrowed from Buddhist Tantras. This exchange has happened from both sides but both like to see themselves as the source. While Kashmiri Shaivaites see the influence of their Tantras in every nook and corner of the Buddhist Pantheon, sometimes quite outrageously for they have the benefit of their counterparts being unfamiliar with Hindu Tantras, the Buddhist scholars do the same, but with greater dignity most of the time. Authors such as Jayaratha and others portray Buddha and Buddhist deities as false gods; Buddhist works adopt a similar tone to demean various Hindu deities. One can refer to the works of brilliant scholars such as Geshe Rinchen, Reginald etc., who have comfortably disproved the flawed theories of others such as Alexis Sanderson who seek to establish Hindu Tantra as the single most source of a class of Buddhist Tantras.
A brilliant team of scholars backed by H H Dalai Lama is currently engaged in bringing out a series of publications on Buddhist Tantras (especially those dear to vajrayana or mantrayana sects) and if I can go by the short preview I have seen, they are fantastic. Coming back to our story, in this nok jhok that took place, some cults in Kashmir created works that they named Tantras and came up with characters like tathAgatamardinI (durgA) and sugatasamhAriNI (kAlI). I even saw an idol of one such form being sold at an emporium at San Francisco. There is also a hymn dedicated to this form of durgA with bad Chandas that claims to be a part of rudrayAmaLa, which obviously is untrue. A Kashmiri upAsaka who gave me this copy explained the term sugata as sugatAsura who assumed the form of Buddha and resorted to himsA. He was accompanied by Vajravarahi (the stava does not refer to his manifestation as samvara however, who is vajravArAhi's consort), who is also an important Hindu deity worshipped not only by nAtha yogis following matsyendra but also by upAsakas of vArAhI in saurAShTra. Then Mother supposedly assumed this form of sugatamardinI to destroy him. The gentleman was not sure about the origin of this tale though. This hardly seemed logical for the stotra is abundant with names of Bodhisattvas described as tathAgata's army and various popular Buddhist concepts made fun of. Apart from such works, there seems to be no description of battle involving the Buddha described as the ninth avatAra of shrImannArAyaNa.