Who composed the Mahishasura Mardini stotram?
Was it Adi Sankaracharya ?
As commented, some says it is attributed to both Ramakrishna Kavi and Adi Shankaracharya. I'm here talking about what I've found:
Mahishasuramardini Stotra is a part of Bhagavatipadyapushpanjalistotra (भगवतीपद्यपुष्पांजलिस्तोत्र) which is written by Ramakrishna Kavi.You can read the full Bhagavati Padya Pushpanjali Stotra here in Sanskrit or transliteration.
It can be seen that After 6th verse of Bhagavati Padya Pushpanjali Stotra, Mahishasur Mardini Stotra starts which have 27 verses and then remains another three verses of Bhagavati Padya Pushpanjali Stotra. Verse 29 mention the author of Stotra who is Ramakrishna Kavi
रमयति किल कर्षस्तेषु चित्तं नराणामवरजवरयस्माद्रामकृष्णः कवीनाम् ।
अकृत सुकृतिगम्यं रम्यपद्यैकहर्म्यं स्तवनमवनहेतुं प्रीतये विश्वमातुः ॥ २९॥
ramayati kila karShasteShu chittaM narANAmavarajavarayasmAdrAmakR^iShNaH kavInAm |
akR^ita sukR^itigamyaM ramyapadyaikaharmyaM stavanamavanahetuM prItaye vishvamAtuH || 29||
Sanskrit documents page on Mahishasura Mardini Stotra also mentions that at the end:
The stotra is part of bhagavatIpadyapuShpA.njalIstotra written by Shri Ramakrishna Kavi.
This stōtram isn't independent . Rather It's totally authenticated by Shastra itself and that to from Śiva Rahasya Mahētihāsa. Not from Purāṇas rather a Mahētihāsa itself. And the stōtram available now in the internet is totally fake and has no Shastra pramanam as it's interpolated from the real Mahiṣāsura Mardini Stotram that is present in Śiva Rahasya Mahētihāsa!!
Let me show the real Mahiṣāsura Mardini Stotram.: Devas chanted this stotram alone for Maata Parvati just after reciting "Upanishad Nirupanam Stuti" for Lord Śiva in Śiva Rahasya Mahētihāsa!!
This is the real Mahiṣāsura Mardini Stotram from ~ Śiva Rahasya Mahētihāsa Amsha-1 Ch-53 recited by Dēvas for Maata Parvati!!
Actually there's no such word called "Viṣṇu Vilasini" rather it's "Śambhu Vilasini" . Literally the next verse says Sitikantha Kutumbini The present of Viṣṇu Vilasini here does not make any sense!!
The people who changed it even tried to show hari hara vaada here putting Viṣṇu Vilasini at the place of Saṃbhū Vilasini and Jiṣṇunutē at the place of Viṣṇunutē.
Viṣṇunutē here means viṣṇu bows down to Maata Parvati but it seems they changed the word with "Jiṣṇunutē" (Indra) - Indra bows down !!
Some people even use "viṣṇu vilasini" here Literally just to show durga related to viṣṇu as her consort Lakshmi or the one who satisfies viṣṇu by giving his bhakti to everyone. Even in the internet they translated it she gives pleasure to viṣṇu. Literally the very next verse says Sitikantha kutumbini (Śiva’s enternal consort) so that verse is a clear Interpolation or it just means She as a sister plays with viṣṇu. But anyways that line is totally a later added line!