The 2011 film Sherlock Holmes: A Game of Shadows (often referred to as Sherlock Holmes 2 ), starring Robert Downey Jr., has been released in Tamil dubbed Official Platforms for Watching
Always ensure you are searching for the correct title. Robert Downey Jr.'s A Game of Shadows is the one you most likely want.
Netflix: Available for streaming in India as part of a standard subscription.
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Since the film is produced by Warner Bros. (and distributed by Village Roadshow), it moves between platforms. Disney+ Hotstar previously hosted the film with multiple dubbed languages. Check their "Search" section for "Sherlock Holmes 2" and filter by language.
Apple TV / iTunes: Available for digital purchase and download through the Apple TV Store.