Hello, 

Yes, you are eligible to do LLM Criminal Law after BA LLB. 

L.L.M Criminal Law is a 3- year post-graduate course, The basic eligibility for the pursuance of the course is L.L.B or B.A.- L.L.B from a recognized university. The average annual course fee charged for the course in India ranges between INR 3 and 5 Lacs, varying across institutes.

Listed below are some of the top institutes offering L.L.M CRIMINAL LAW course 

• National Law School of India University (NLSIU)Bangalore
• Faculty of Law, University of Delhi, New Delhi 
• NALSAR University of Law, Hyderabad
• The National Law Institute University (NLIU), Bhopal
•  Symbiosis Law School, Pune

Some of the major entrance examinations conducted in India for admission to L.L.M. in Criminal Law are listed here.

• CLAT PG (Common Law Admission Test for L.L.M. course)
• AILET PG (All India Law Entrance Test for L.L.M. course)
• ILI CAT (Indian Law Institute Common Admission Test)
• IPU CET (IP University L.L.M. Entrance Exam).

Hope, this helps. 

Thank you!