Biblatex: Two bibliographies with different styles and sortings

If you pass the option labelnumber to biblatex you can use numeric citations even with style=alphabetic.

The cite command can switch based on keywords, so you can use \cite for all entries regardless of keyword.

For the numeric bibliography we will have to define a new bibliography environment that prints numeric citations. bibliographyNUM is directly copied from numeric.bbx. To set the sorting for the bibliography, just say

\newrefcontext[sorting=none]
\printbibliography[env=bibliographyNUM, title=References, keyword=secondary, resetnumbers]

before the numeric bibliography. The previous bibliography will use the global sorting scheme anyt that is appropriate for alpha-style bibliography. In case it is necessary to keep the sorting scheme assignment local (because the numeric bibliography comes before the alpha bibliography), you would use

\begin{refcontext}[sorting=none]
\printbibliography[env=bibliographyNUM, title=References, keyword=secondary, resetnumbers]
\end{refcontext}

MWE

\documentclass{article}
\usepackage[style=alphabetic, labelnumber, defernumbers=true,  backend=biber]{biblatex}
\usepackage{hyperref}

% Append keywords to identify different bibliography entries.
% appendstrict only appends if the field is nonempty,
% we use that to add a comma to avoid mushing together two keywords
\DeclareSourcemap{
  \maps[datatype=bibtex, overwrite]{
    \map{
      \perdatasource{biblatextest1.bib}
      \step[fieldset=KEYWORDS, fieldvalue={, }, appendstrict]
      \step[fieldset=KEYWORDS, fieldvalue=primary, append]
    }
    \map{
      \perdatasource{biblatextest2.bib}
      \step[fieldset=KEYWORDS, fieldvalue={, }, appendstrict]
      \step[fieldset=KEYWORDS, fieldvalue=secondary, append]
    }
  }
}

\DeclareFieldFormat{labelnumberwidth}{\mkbibbrackets{#1}}
\renewbibmacro*{cite}{%
  \printtext[bibhyperref]{%
    \printfield{labelprefix}%
    \ifkeyword{secondary}
      {\printfield{labelnumber}}
      {\printfield{labelalpha}%
       \printfield{extraalpha}}}}

\defbibenvironment{bibliographyNUM}
  {\list
     {\printtext[labelnumberwidth]{%
        \printfield{labelprefix}%
        \printfield{labelnumber}}}
     {\setlength{\labelwidth}{\labelnumberwidth}%
      \setlength{\leftmargin}{\labelwidth}%
      \setlength{\labelsep}{\biblabelsep}%
      \addtolength{\leftmargin}{\labelsep}%
      \setlength{\itemsep}{\bibitemsep}%
      \setlength{\parsep}{\bibparsep}}%
      \renewcommand*{\makelabel}[1]{\hss##1}}
  {\endlist}
  {\item}

\begin{filecontents}{biblatextest1.bib}
@BOOK{BookA03,
  author    = {Author Aaa},
  title     = {Some Title},
  publisher = {Some Publisher},
  year      = 2003,
  keywords  = {hello},
}
@BOOK{BookB02,
  author    = {Author Bbb},
  title     = {Some Title},
  publisher = {Some Publisher},
  year      = 2002,
}
\end{filecontents}
\begin{filecontents}{biblatextest2.bib}
@MISC{LinkC04,
  author    = {Author Ccc},  
  title     = {Some Title},
  year      = 2004,
  url       = {www.test1.com/bild.jpg},
  keywords  = {bye},
}
@MISC{LinkD01,
  author  = {Author Ddd},
  title   = {Some Title},
  year    = 2001,
  url     = {www.test2.com/bild.jpg},
}
\end{filecontents}
\addbibresource{biblatextest1.bib}
\addbibresource{biblatextest2.bib}

\begin{document}
The first two citations \cite{LinkD01} and \cite{BookB02}. 
The others are \cite{LinkC04} and \cite{BookA03}.

\printbibliography[title=Bibliography, keyword=primary]

\newrefcontext[sorting=none]
\printbibliography[env=bibliographyNUM, title=References, keyword=secondary, resetnumbers]
\end{document}