Concept:
Tripurantaka is a form of Lord Shiva.
In this form, Shiva destroys the three cities of the demons.
The theme is important in Shaiva art and temple painting.
Step 1: Check Brihadeshwara Temple.
Brihadeshwara Temple at Tanjore is a major Chola Shaiva temple.
It is famous for mural paintings, including Shaiva themes.
So:
\[
A = \text{Correct}
\]
Step 2: Check Virupaksha Temple, Hampi.
Virupaksha Temple at Hampi is also connected with important mural traditions and Shaiva themes.
So:
\[
C = \text{Correct}
\]
Step 3: Eliminate the other options.
Kailashnath Temple, Vaikuntha Perumal Temple and Varadaraja Temple are not selected as the correct pair in this question.
Step 4: Final conclusion.
The famous Tripurantaka painting is associated with:
\[
A,\ C
\]
Hence:
\[
\boxed{\text{(C) A and C only}}
\]