REVISED APPROACH (\stackinset)
Here, I just \stackinset any number of \hyperrefed \makeboxes to encompass the desired portion of the base image. The \stackinset can be specified relative to the l,c,r horizontal anchors and the t,c,b vertical anchors.
\documentclass{article}
\usepackage{graphicx}
\usepackage{hyperref,stackengine}
\begin{document}
\begin{figure}
\centering
\stackinset{l}{10pt}{t}{20pt}{\hyperref[topleft]{\makebox(100,100){}}}{%
\stackinset{r}{30pt}{t}{40pt}{\hyperref[topright]{\makebox(50,40){}}}{%
\stackinset{l}{40pt}{b}{50pt}{\hyperref[bottomleft]{\makebox(70,20){}}}{%
\stackinset{r}{110pt}{b}{70pt}{\hyperref[bottomright]{\makebox(40,80){}}}{%
\includegraphics[width=\linewidth]{example-image}}}}}
\end{figure}
\clearpage
\pagebreak
\section{Section 1}
\label{topleft}
Some Text
\pagebreak
\section{Section 2}
\label{topright}
Some Text
\pagebreak
\section{Section 3}
\label{bottomleft}
Some Text
\pagebreak
\section{Section 4}
\label{bottomright}
Some Text
\end{document}

ORIGINAL APPROACH (\clipbox)
Here I use \clipbox to partition the figure into 4 [unequal-sized] quadrants, though there is, in theory, no reason you can't slice it into any number of rectangles.
I don't know how, but I am sure hyperref provides the means to make the \hyperref bounding box invisible.
\documentclass{article}
\usepackage{graphicx}
\usepackage{hyperref,trimclip,stackengine}
\begin{document}
\begin{figure}
\centering
\setbox0=\hbox{\includegraphics[width=\linewidth]{example-image}}
\stackunder[0pt]{%
\hyperref[topleft]{\clipbox{0pt .4\ht0{} .3\wd0{} 0pt}{\copy0}}%
\hyperref[topright]{\clipbox{.7\wd0{} .4\ht0{} 0pt 0pt}{\copy0}}}{%
\hyperref[bottomleft]{\clipbox{0pt 0pt .3\wd0{} .6\ht0}{\copy0}}%
\hyperref[bottomright]{\clipbox{.7\wd0{} 0pt 0pt .6\ht0}{\copy0}}}
\end{figure}
\clearpage
\pagebreak
\section{Section 1}
\label{topleft}
Some Text
\pagebreak
\section{Section 2}
\label{topright}
Some Text
\pagebreak
\section{Section 3}
\label{bottomleft}
Some Text
\pagebreak
\section{Section 4}
\label{bottomright}
Some Text
\end{document}
A click in separate corners of the image will take you to different pages in the document.
