The correct answer to the question is option 'C', Tuluvad dynasty.

The Battle of Talikota, also known as the Battle of Rakshasa Tangadi, took place on January 26, 1565. It was a significant battle in the history of the Vijayanagara Empire, as it led to the downfall of the empire.

The Battle of Talikota was fought between the forces of the Deccan Sultanates coalition, consisting of the Bijapur Sultanate, the Ahmadnagar Sultanate, the Golconda Sultanate, and the Bidar Sultanate, against the Vijayanagara Empire. The Deccan Sultanates were determined to bring an end to the Vijayanagara Empire, which had been a dominant power in Southern India for several centuries.

Now, let's delve into the ruling dynasty of the Vijayanagara Empire during the Battle of Talikota:

Tuluvad Dynasty:
- The Tuluvad dynasty was ruling in the Vijayanagara Empire at the time of the Battle of Talikota.
- The Tuluvad dynasty came to power after the decline of the Sangama dynasty, which had ruled the empire for several generations.
- The Tuluvad dynasty was established by Vira Narasimha, who was the younger brother of the last Sangama dynasty ruler, Rama Raya.
- Vira Narasimha assumed the title of "Vira Narasimha Raya" and founded the Tuluvad dynasty in 1560.
- He tried to consolidate the empire and strengthen its defenses, but he faced numerous challenges from the Deccan Sultanates.
- Unfortunately, Vira Narasimha Raya's reign was short-lived, as he was killed in the Battle of Talikota in 1565.
- The defeat of the Vijayanagara Empire in this battle marked the end of their rule and the beginning of a period of decline and fragmentation.

In conclusion, the Tuluvad dynasty was ruling in the Vijayanagara Empire at the time of the Battle of Talikota. The battle resulted in the downfall of the empire and the end of their reign in Southern India.