NP Hardness of Diagonal Language.

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How do I prove that Diagonal Language is NP-Hard and it is not NP-Complete. Where diagonal language(Ld) is the language where a Turing Machine does not accept its own encoding as a string.

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To show that this language is not in NP, you prove that it is not decidable at all (and everything in NP is decidable).

To show that this language is NP-hard, try to come up with a transformation of Turing machines that turns a non-deterministic Turing machine with input into a deterministic Turing machine with no input such that the latter accepts iff the former rejects for every guess. The straight-forward way of doing so will be doable in polynomial time, and hence work here.