Yeah for the best roles in MBB and the FO ones, not only top tier degree but also certain spikes in your CV, decent no of achievements is what I've heard. Also consistency in multiple rounds of interviews that they have. It's really hard to get an interview without a partner referral for a good role is what I've understood by lurking on the consulting subreddit.
Yes always hard to get into MBB. You need to be from a a top IIT or IIM at exit to be able to get in. They only visit select campuses