Wave to welcome pained daughter? Thick-skinned sort (9)

I believe the answer is:

pachyderm

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'thick-skinned sort' is the definition.
(I know that pachyderm are thick-skinned)

I cannot understand how the rest of the clue works.

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(Other definitions for pachyderm that I've seen before include "jumbo" , "Elephant, perhaps" , "Insensitive sort" , "One thick-skinned" , "Large hoofed animal with a very thick skin" .)

I've seen this clue in The Independent.

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