No, there's no API route that gives you a user's tag specific reputation information. The /users/{ids}/tags route only returns the combined count of questions and answers that a user has posted in a tag, but not the reputation information that you can get on the user profile tags tab. (Note: There's an app at Badge Status for a particular Tag in Stackoverflow that scrapes that page to get the information you're looking for.)
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Bill the Lizard
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