I haven't yet found a breakdown of these costs, but did find this 2011 message from Dipak Dasgupta, the Principal Economic Adviser of their Ministry of Finance, who was quoted in the Hindu Times article. He gives this table:
I've written to ask for more information.
I agree there are reasons to be skeptical about India's self-reported costs adaptation. For example, this FAQ from the Climate Change Finance division of their Finance Ministry is heavy with discussion of adaptation financing coming from developed countries (viz. not India) for developing countries (viz. India). Just having a "Climate Change Finance" division already tells you something about where they're coming from. (That's not a comment about the morals and ethics of climate change impacts, just an observation about their emphasis.) And it's not just adaptation; in the same document as above, Dasgupta writes:
Costs: India will have to sustain a growth rate of 8-9% for the next 20 years to eradicate poverty and meet its other human development goals. Meeting the energy requirements for growth of this magnitude in a sustainable manner presents a major challenge. The need to accommodate India‟s environment pledges is expected to impact growth figures if no external financial support is extended. The investments so far have not been enough to bridge the gap in the need and availability of resources, and the future is likely to be much harder requiring massive amount of resources, technology transfers and choices, research and development, incentives, etc. , reinforcing the fact that this ambitious pledge of 20-25% emission intensity reduction is not going to be costless.