ATMA

You can appear for exam like IIFT, I think in India no other college is as good as IIFT (Indian institute of foreign trade) for international business.

There are lots of colleges providing you MBA but according to MAT only few best colleges are there which accepts 95 above percentile.
It is better for you to check colleges by your percentile on Shiksha instead of asking others because no one will tell you the best college, but do MBA from Bangalore or Pune.

The following are some good colleges in and around Mumbai, which accept the ATMA exam score:
Vivekanand Education Society's Institute of Management Studies & Research (VESIM), Chembur
Thakur Institute of Management Studies and Research (TIMSR), Kandivali
Welingkar Institute of Management Development & Research (WeSchool), Matunga
SIES College of Management Studies (SIESCOMS), Nerul
Sydenham Institute of Management Studies, Research and Entrepreneurship Education (SIMSREE), Churchgate
MET Institute of Management (MET IOM), Bandra

KITSOM, AIMS are two good colleges where you have decent chances. Check list of top MBA colleges accepting ATMA scores.
https://www.shiksha.com/mba/ranking/top-mba-colleges-india-accepting-atma/2-2-0-0-9180

Now the date of applying in welingkar is over.

Sorry the extended date is over now.

Hello, last year the cut off for ATMA was 99.75 percentile. So it is a little difficult for you to get the seat.

You need to go the insearch website and fill the form for admission and then submit whatever documents that are needed with the scores.