According to various movie aggregator sites, "Batman Begins" is currently available on the following OTT platforms with Tamil language options:
"Irudalilae neethi. Paathaiyilae mutru. Gotham ku oru pudhu poraali." (Darkness as justice. The path as an end. A new warrior for Gotham.) Batman Begins 2005 Tamil Dubbed
Luckily, the is available in Tamil, allowing you to binge-watch the complete saga over a weekend. According to various movie aggregator sites, "Batman Begins"