Since the watershed is huge, I am unable to find the required Landsat scenes so that I could mosaic them into one raster and then do further analysis on them using ArcGIS.
Check the (Hydrological data and maps based on SHuttle Elevation Derivatives at multiple Scales it has information about all the river systems in the world and also modified elevation data (DEM)
You have to extract watershed from DEM (SRTM 90m, SRTM 30m (available on hydrosheds web) or ASTER 30m using GIS analysis toolbox (like hydrological analysis in ArcGIS)
Try using the Hydrosheds platform (https://www.hydrosheds.org/products). It provides a variety of GIS data with global watershed / river / river basin / atlas coverage.