Step 1: Understanding the Concept:
The Vijayanagara Empire reached its peak under the Tuluva dynasty, specifically during the reign of its most illustrious ruler.
Step 2: Detailed Explanation:
Krishnadevaraya ($1509-1529$) is celebrated as the greatest ruler of Vijayanagara.
He was a prolific builder who established the suburban township of Nagalapuram, named in honor of his mother, Nagala Devi.
His reign was a period of great prosperity and artistic flourishing, attracting many foreign travelers.
Significant accounts from travelers like Duarte Barbosa and Domingo Paes provide us with rich details about the city's fortification, markets, and the king's court during his era.
Step 3: Final Answer:
The description points towards Krishnadevaraya. Hence, option (b) is the correct answer.