Step 1: Understand the question.
The question asks about the shipyard where INS Tushil, a stealth guided missile frigate, was built.
Step 2: Examine each option.
- Option A: Hong Kong United Dockyards is not the shipyard for INS Tushil.
- Option B: Guangzhou Shipyard International, China, was not responsible for building INS Tushil.
- Option C: Correct. Yantar Shipyard, Russia, built INS Tushil.
- Option D: Naval Group Shipyard, France, did not build this particular frigate.
- Option E: Navantia Shipyard, Spain, did not build this frigate either.
Step 3: Conclude.
The correct answer is Yantar Shipyard, Russia.
Final Answer:
\[
\boxed{\text{C}}
\]