Step 1: Question Analysis.
The query concerns the construction location of the INS Tushil, a stealth guided missile frigate.
Step 2: Option Evaluation.
- Option A: Hong Kong United Dockyards is excluded as the builder of INS Tushil. - Option B: Guangzhou Shipyard International, China, did not construct INS Tushil. - Option C: Confirmed. Yantar Shipyard, Russia, is the builder of INS Tushil. - Option D: Naval Group Shipyard, France, did not build this frigate. - Option E: Navantia Shipyard, Spain, also did not build this frigate.
Step 3: Determination.
The correct shipyard is Yantar Shipyard, Russia.
Final Answer: \[\boxed{\text{C}}\]