I'd go with clipping the image and include it four times (this will have no impact on the final PDF size, because the resource will be loaded just once). With \clipbox*
of the trimclip
package you don't even need to know the image size.
\documentclass{article}
\usepackage{subcaption,graphicx,trimclip,hyperref,cleveref}
\begin{document}
\begin{figure}
\centering
\subcaptionbox{Top left\label{tl}}{%
\clipbox*{0 {.5\height} {.5\width} {1\height}}{%
\includegraphics[width=8cm]{duck}%
}%
}\qquad
\subcaptionbox{Top right\label{tr}}{%
\clipbox*{{.5\width} {.5\height} {1\width} {1\height}}{%
\includegraphics[width=8cm]{duck}%
}%
}
\medskip
\subcaptionbox{Bottom left\label{bl}}{%
\clipbox*{0 0 {.5\width} {.5\height}}{%
\includegraphics[width=8cm]{duck}%
}%
}\qquad
\subcaptionbox{Bottom right\label{br}}{%
\clipbox*{{.5\width} 0 {1\width} {.5\height}}{%
\includegraphics[width=8cm]{duck}%
}%
}
\caption{A split duck}
\end{figure}
\end{document}

A fuller example showing that the references are as expected.
\documentclass{article}
\usepackage{subcaption,graphicx,trimclip}
\usepackage[colorlinks]{hyperref}
\usepackage[nameinlink]{cleveref}
\captionsetup[subfigure]{subrefformat=simple,labelformat=simple}
\renewcommand\thesubfigure{\alph{subfigure}}
\crefdefaultlabelformat{#2#1#3}
%options for equations
\creflabelformat{equation}{#2#1#3}
\crefformat{equation}{#2Eq.~#1#3}
\Crefformat{equation}{#2Equation~#1#3}
\crefmultiformat{equation}{#2Eqs.~#1#3}%
{ and~#2#1#3}{, #2#1#3}{ and~#2#1#3}
%options for enumerations
\creflabelformat{enumi}{#2(#1)#3}
\crefformat{enumi}{#2(#1)#3}
\Crefformat{enumi}{#2(#1)#3}
%options for figures
\creflabelformat{figure}{#2#1#3}
\crefformat{figure}{#2Fig.~#1#3}
\Crefformat{figure}{#2Figure~#1#3}
\crefmultiformat{figure}{#2Fiqs.~#1#3}%
{ and~#2#1#3}{, #2#1#3}{ and~#2#1#3}
\begin{document}
A reference to \cref{global}, then to
\cref{tl}, \cref{tr}, \cref{bl} and \cref{br}.
\begin{figure}[htp]
\centering
\subcaptionbox{\label{tl}}{%
\clipbox*{0 {.5\height} {.5\width} {1\height}}{%
\includegraphics[width=8cm]{duck}%
}%
}\qquad
\subcaptionbox{\label{tr}}{%
\clipbox*{{.5\width} {.5\height} {1\width} {1\height}}{%
\includegraphics[width=8cm]{duck}%
}%
}
\medskip
\subcaptionbox{\label{bl}}{%
\clipbox*{0 0 {.5\width} {.5\height}}{%
\includegraphics[width=8cm]{duck}%
}%
}\qquad
\subcaptionbox{\label{br}}{%
\clipbox*{{.5\width} 0 {1\width} {.5\height}}{%
\includegraphics[width=8cm]{duck}%
}%
}
\caption{A split duck}\label{global}
\end{figure}
\end{document}

The following code will create links also without clipping the figure; add
\newcommand{\labelphantom}[1]{%
\parbox{0pt}{\phantomsubcaption\label{#1}}%
}
in your preamble and then type
A reference to \cref{global2}, then to
\cref{tl2}, \cref{tr2}, \cref{bl2} and \cref{br2}.
\begin{figure}[htp]
\centering
\labelphantom{tl2}%
\labelphantom{tr2}%
\labelphantom{bl2}%
\labelphantom{br2}%
\includegraphics[width=8cm]{duck}%
\caption{A split duck}\label{global2}
\end{figure}

\phantomsubcaption
s and appropriate\label
s you can refer to later anywhere inside the figure's code.\phantomsubcaption
s the figure number also goes up, leading to wrong figure numbers in the following figures. Also, only adding additional\label{fig: 1_a}
s does not work, as a reference to them via\cref{fig: 1_a}
reads "section 1.1" and not "fig 1a".