The probably simplest option is
\documentclass[border=10pt,multi,tikz]{standalone}
\begin{document}
\begin{tikzpicture}
\begin{scope}[opacity=0.2]
\node [inner sep=0pt,clip,rounded corners=0.1cm] {\includegraphics[width=0.85\textwidth,keepaspectratio]{example-image-a}};
\end{scope}
\end{tikzpicture}
\end{document}

I never understood why there is this restriction because, as seen above, TikZ actually can use such paths for clipping.
However, there are situations in which a simple scope may not be sufficient. In these you can save and reuse the path, and according to my experience that works. (I increased the radius of the rounded corners to make it very visible that it does work)
\documentclass[border=10pt,multi,tikz]{standalone}
\makeatletter % https://tex.stackexchange.com/a/38995/121799
\tikzset{
use path/.code={\pgfsyssoftpath@setcurrentpath{#1}}
}
\makeatother
\begin{document}
\begin{tikzpicture}
\node [inner sep=0pt,opacity=0,rounded corners=0.3cm,save path=\mypath]
{\includegraphics[width=0.85\textwidth,keepaspectratio]{example-image-a}};
\clip[use path=\mypath];
\node [inner sep=0pt,opacity=0.2]
{\includegraphics[width=0.85\textwidth,keepaspectratio]{example-image-a}};
\end{tikzpicture}
\end{document}

I agree that all this extra effort should not be necessary but at least it works and satisfies "no extra packages".
If you do not like the \makeatletter stuff, you could use (I learned this from Kpym in a comment)
\documentclass[border=10pt,multi,tikz]{standalone}
\tikzset{use path/.code={\pgfsetpath{#1}}}
\begin{document}
\begin{tikzpicture}
\node [inner sep=0pt,opacity=0,rounded corners=0.3cm,save path=\mypath]
{\includegraphics[width=0.85\textwidth,keepaspectratio]{example-image-a}};
\clip[use path=\mypath];
\node [inner sep=0pt,opacity=0.2]
{\includegraphics[width=0.85\textwidth,keepaspectratio]{example-image-a}};
\end{tikzpicture}
\end{document}
And yet another option which does not use an explicit clip (but should be used with care) is
\documentclass[border=10pt,multi,tikz]{standalone}
\begin{document}
\begin{tikzpicture}
\node [inner sep=0pt,rounded corners=0.3cm,
path picture={\node[opacity=0.2] at (path picture bounding box.center)
{\includegraphics[width=0.85\textwidth,keepaspectratio]{example-image-a}};}]
{\phantom{\includegraphics[width=0.85\textwidth,keepaspectratio]{example-image-a}}};
\end{tikzpicture}
\end{document}
That is, a path picture effectively clips, which brings us back to the statement that there might be no deep reason for the complaint "no extra options are allowed" at least for harmless options.
extra options not allowed for clipping path- as one could have expected. -so nothing to do with corners and opacity at the same time. – hpekristiansen May 05 '19 at 21:06