Some online resources that discuss and evaluate R. Mordechai Breuer’s approach to biblical scholarship:
1. R. Moshe J. Bernstein, “The Orthodox Jewish Scholar and Jewish Scholarship: Duties and Dilemmas” in The Torah u-Madda Journal, vol. 3 pp. 23-24 (link)
2. R. Shalom Carmy, “Introducing Rabbi Breuer” in Shalom Carmy ed., Modern Scholarship in the Study of Torah: Contributions and Limitations (link). Note that this volume also had a presentation by R. Breuer and a critique by R. Shnayer Leiman, neither of which are currently available online.
3. Meir Ekstein, “Rabbi Mordechai Breuer and Modern Orthodox Biblical Commentary” in Tradition 33:3 (1999) (link)
4. R. Moshe Lichtenstein, “Ahas Diber Elokim, Shetayim Zu Shamati?” in Daf Kesher Le-Talmidei Yeshivas Har Etzion no. 851 (link)
5. R. Yoel Bin-Nun, “Ahas Diber Elokim, Shetayim Zu Shamati!” in Daf Kesher Le-Talmidei Yeshivas Har Etzion no. 863 (link)
6. R. Mordechai Breuer, “Bikores Ha-Mikra Ve-Ha-Emunah Ba-Torah Min Ha-Shamayim” in Daf Kesher Le-Talmidei Yeshivas Har Etzion no. 864 (link)
7. R. Chaim Navon, “Biblical Criticism” (link)