In light of the comments, I have revised my answer, the old version is further down.
We first need to define a new wrapper for a marker-less footnote
\makeatletter
\newrobustcmd{\mkbibblfootnote}[1]{%
\iftoggle{blx@footnote}
{\blx@warning{Nested notes}%
\addspace\mkbibparens{#1}}
{\unspace
\ifnum\blx@notetype=\tw@
\expandafter\@firstoftwo
\else
\expandafter\@secondoftwo
\fi
{\csuse{blx@theendnote}{\protecting{\blxmkbibnote{end}{#1}}}}
{\csuse{blfootnote}{\protecting{\blxmkbibnote{foot}{#1}}}}}}
\newcommand\blfootnote[1]{\begingroup\let\thefootnote\relax\footnotetext{#1}\endgroup}
\makeatother
\megafullcite now prints the alphabetic label and, if it is the first time this work was cited - for that feature, we need citetracker in any of its flavours (see § 3.1.2.3, p. 54 of the biblatex documentation); in the MWE I chose strict -, also prints a marker-less footnote with the alphabetic label, the author name, year and title.
The footnote for \megafullcite{wilde} is
[Wil99] Wilde (1899), The Importance of Being Earnest: A Trivial Comedy
for Serious People.
\DeclareCiteCommand{\megafullcite}
{\usebibmacro{prenote}}
{\mkbibbrackets{\usebibmacro{cite}}%
\ifciteseen{}
{\mkbibblfootnote{%
\mkbibbrackets{\usebibmacro{cite}}%
\setunit{\addspace}%
\usebibmacro{morecite}}}}
{\multicitedelim}
{\usebibmacro{postnote}}
\newbibmacro*{morecite}{%
\printnames{labelname}%
\setunit{\addspace}%
\printfield[parens]{year}%
\setunit{\nametitledelim}%
\printfield[citetitle]{labeltitle}}
MWE
\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[british]{babel}
\usepackage{csquotes}
\usepackage[style=alphabetic,backend=biber,citetracker=strict]{biblatex}
\usepackage{hyperref}
\addbibresource{biblatex-examples.bib}
\makeatletter
\newrobustcmd{\mkbibblfootnote}[1]{%
\iftoggle{blx@footnote}
{\blx@warning{Nested notes}%
\addspace\mkbibparens{#1}}
{\unspace
\ifnum\blx@notetype=\tw@
\expandafter\@firstoftwo
\else
\expandafter\@secondoftwo
\fi
{\csuse{blx@theendnote}{\protecting{\blxmkbibnote{end}{#1}}}}
{\csuse{blfootnote}{\protecting{\blxmkbibnote{foot}{#1}}}}}}
\newcommand\blfootnote[1]{\begingroup\let\thefootnote\relax\footnotetext{#1}\endgroup}
\makeatother
\DeclareCiteCommand{\megafullcite}
{\usebibmacro{prenote}}
{\mkbibbrackets{\usebibmacro{cite}}%
\ifciteseen{}
{\mkbibblfootnote{%
\mkbibbrackets{\usebibmacro{cite}}%
\setunit{\addspace}%
\usebibmacro{morecite}}}}
{\multicitedelim}
{\usebibmacro{postnote}}
\newbibmacro*{morecite}{%
\printnames{labelname}%
\setunit{\addspace}%
\printfield[parens]{year}%
\setunit{\nametitledelim}%
\printfield[citetitle]{labeltitle}}
\begin{document}
Lorem ipsum \megafullcite{wilde} again \megafullcite{wilde}.
Lorem ipsum \megafullcite{wilde,cicero}.
Lorem ipsum \megafullcite{baez/article,baez/online}.
\printbibliography
\end{document}

This is the old version of the answer, it implements a more verbose version with \fullcite
We can define two new citation commands
\megafootfullcite will print the alphabetic label and the full bibliography entry in the footnote.
\DeclareCiteCommand{\megafootfullcite}[\mkbibfootnote]
{\usebibmacro{prenote}}
{\mkbibbrackets{\usebibmacro{cite}}%
\setunit{\addspace}%
\usedriver
{\DeclareNameAlias{sortname}{default}}
{\thefield{entrytype}}}
{\multicitedelim}
{\usebibmacro{postnote}}
so \megafootfullcite{wilde} gives a footnote with the contents
[Wil99] Oscar Wilde. The Importance of Being Earnest: A Trivial Comedy for Serious
People. Leonard Smithers and Company, 1899.
\megafullcite prints the alphabetic label in the text and adds a footnote for the full bibliography entry.
\DeclareCiteCommand{\megafullcite}
{\usebibmacro{prenote}}
{\mkbibbrackets{\usebibmacro{cite}}%
\mkbibfootnote{\usedriver
{\DeclareNameAlias{sortname}{default}}%
{\thefield{entrytype}}}}
{\multicitedelim}
{\usebibmacro{postnote}}
or
\DeclareCiteCommand{\megafullcite}
{\usebibmacro{prenote}}
{\mkbibbrackets{\usebibmacro{cite}}%
\mkbibfootnote{%
\mkbibbrackets{\usebibmacro{cite}}%
\setunit{\addspace}%
\usedriver
{\DeclareNameAlias{sortname}{default}}%
{\thefield{entrytype}}}}
{\multicitedelim}
{\usebibmacro{postnote}}
The two version above differ in that the latter will put the alphabetic label into the footnote as well, the former will not repeat the label in the footnote.
MWE
\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[british]{babel}
\usepackage{csquotes}
\usepackage[style=alphabetic]{biblatex}
\usepackage{hyperref}
\addbibresource{biblatex-examples.bib}
\DeclareCiteCommand{\megafootfullcite}[\mkbibfootnote]
{\usebibmacro{prenote}}
{\mkbibbrackets{\usebibmacro{cite}}%
\setunit{\addspace}%
\usedriver
{\DeclareNameAlias{sortname}{default}}%
{\thefield{entrytype}}}
{\multicitedelim}
{\usebibmacro{postnote}}
\DeclareCiteCommand{\megafullcite}
{\usebibmacro{prenote}}
{\mkbibbrackets{\usebibmacro{cite}}%
\mkbibfootnote{\usedriver
{\DeclareNameAlias{sortname}{default}}%
{\thefield{entrytype}}}}
{\multicitedelim}
{\usebibmacro{postnote}}
\begin{document}
Lorem ipsum\megafootfullcite{wilde} and \megafullcite{wilde}.
Lorem ipsum\megafootfullcite{wilde,cicero} and \megafullcite{wilde,cicero}.
\printbibliography
\end{document}

style=alphabetic? – moewe Mar 16 '14 at 17:22