In the biopic movie based on the life of the famous mathematician, Shakuntala Devi, the role of Shakuntala Devi was played by Vidya Balan. It is important to note that the other options mentioned are incorrect.

Option 1: Madhuri Dixit, a popular Bollywood actress, did not portray the role of Shakuntala Devi in the biopic.

Option 2: Rani Mukherjee, another well-known Bollywood actress, also did not play the role of Shakuntala Devi.

Option 3: Tabu, a highly regarded actress, was not cast as Shakuntala Devi.

Therefore, the correct answer is option 4, Vidya Balan. She convincingly portrayed the character of Shakuntala Devi in the biopic, showcasing her talent and dedication as an actress. It is essential to pay attention to the details and eliminate the incorrect options to arrive at the correct answer.