Hyperref, bibentry & natbib conflict - incorrect hyperlink

Wrap the \bibentry in NoHypers i.e.

\begin{NoHyper}\bibentry{elvis}\end{NoHyper}

The hyperlink now points to the correct entry in the references.

I'd add this to the top answer's comment thread, but I do not yet have the requisite reputation for commenting. With regard to rubenvb's request in response to wrapping \bibentry in a NoHyper environment:

This does indeed fix the internal document link, but if there is a hyperlink in the bibliography entry itself, it is not hyperlinked anymore, unfortunately. A way to have both would be brilliant.

You can eschew NoHyper for a simple solution to correctly hyperlink citations to their corresponding non-\bibentry reference items (while maintaining existing hyperlinks within the \bibentry like URLs):

In your .bib file (or if you've defined your bibliographic entries in your preamble), duplicate those references in full and add some differentiating text in the citekey. I like to add -in to the end of the citekeys I'll use for \bibentry items, since they'll be incorporated -in the text. Then, add the multibib environment to your .tex file as described in this answer. If you try to use multibib without duplicating the .bib entry of interest, citations will still jump to \bibentry instead of your bibliography.

MWE

Broken hyperlinks

test.bib file:

@article{Lee:2011ct,
author = {Lee, Hun and Lee, Kangsun and Ahn, Byungwook and Xu, Jing and Xu, Linfeng and Oh, Kwang W},
title = {{A new fabrication process for uniform SU-8 thick photoresist structures by simultaneously removing edge bead and air bubbles}},
journal = {Journal of Micromechanics and Microengineering},
year = {2011},
volume = {21},
number = {12},
pages = {125006--9},
month = nov,
doi = {10.1088/0960-1317/21/12/125006},
read = {Yes},
date-added = {2018-06-21T17:15:45GMT},
url = {http://stacks.iop.org/0960-1317/21/i=12/a=125006?key=crossref.dabe730af97ae5fbb7d5b6bb62b8eb90}}

test.tex file:

\documentclass{article}
\usepackage{natbib}
\usepackage{hyperref}
\usepackage{bibentry}

\begin{document}
\nobibliography*

Here is a citation \citet{Lee:2011ct}

Here is the full entry \bibentry{Lee:2011ct}

\newpage

\bibliography{test}
\bibliographystyle{abbrvnat}

\end{document}

With this, we'll see improper hyperlinking from the first instance of \citet to the \bibentry (instead of the References section on the next page).

Fixed hyperlinks

This is easily resolved by duplicating and modifying our .bib item that we want to include as a \bibentry and adjusting the .tex file:

test.bib file:

@article{Lee:2011ct,
author = {Lee, Hun and Lee, Kangsun and Ahn, Byungwook and Xu, Jing and Xu, Linfeng and Oh, Kwang W},
title = {{A new fabrication process for uniform SU-8 thick photoresist structures by simultaneously removing edge bead and air bubbles}},
journal = {Journal of Micromechanics and Microengineering},
year = {2011},
volume = {21},
number = {12},
pages = {125006--9},
month = nov,
doi = {10.1088/0960-1317/21/12/125006},
read = {Yes},
date-added = {2018-06-21T17:15:45GMT},
url = {http://stacks.iop.org/0960-1317/21/i=12/a=125006?key=crossref.dabe730af97ae5fbb7d5b6bb62b8eb90}}

@article{Lee:2011ct-in,
author = {Lee, Hun and Lee, Kangsun and Ahn, Byungwook and Xu, Jing and Xu, Linfeng and Oh, Kwang W},
title = {{A new fabrication process for uniform SU-8 thick photoresist structures by simultaneously removing edge bead and air bubbles}},
journal = {Journal of Micromechanics and Microengineering},
year = {2011},
volume = {21},
number = {12},
pages = {125006--9},
month = nov,
doi = {10.1088/0960-1317/21/12/125006},
read = {Yes},
date-added = {2018-06-21T17:15:45GMT},
url = {http://stacks.iop.org/0960-1317/21/i=12/a=125006?key=crossref.dabe730af97ae5fbb7d5b6bb62b8eb90}}

test.tex file:

\documentclass{article}
\usepackage{natbib}
\usepackage{hyperref}
\usepackage{bibentry}
\usepackage{natbib}
\usepackage{multibib}
\newcites{q}{References}

\begin{document}
\nobibliography*

Here is a citation \citetq{Lee:2011ct}

Here is the full entry \bibentry{Lee:2011ct-in}

\newpage

\bibliographystyleq{abbrvnat}
\bibliographyq{test.bib}
\bibliographystyle{abbrvnat}
\nobibliography{test.bib}

\end{document}

This produces your desired output: the in-text citation links to the bibliography, and the URL in the \bibentry item is still functional without being hyperlinked to the in-text citation. To compile this .tex file, use the following build order:

pdflatex test.tex
bibtex q
bibtex test
pdflatex test
pdflatex test

I know it's been almost six years since this was first asked, but I recently found this solution useful and wanted it to be available for anyone else who might come across this thread.