I haven't tested this exhaustively, and it probably doesn't work for some crazier titles with @inbook with booktitle or other extras that are similar.
Basically, I have added a flag that checks when we are in the bibliography where it is desired to have the title appear first. Then for those bibitems, we add a new title bibmacro to the beginning of the entry, and clear out the original title bibmacro. For other items with extra title fields, you may have to clear other fields out as well, depending on how you want it to work. (Some entry types don't use \usebibmacro{title}, but use \usebibmacro{maintitle+title}, for example; this does not take that into account.)
I added a few extra entries to demonstrate use.
Code
\documentclass{article}
\usepackage{biblatex}
\usepackage{etoolbox} % For boolean flags
\DeclareBibliographyCategory{cited}
\AtEveryCitekey{\addtocategory{cited}{\thefield{entrykey}}}
% Boolean flags to detect environment
\newbool{titlefirst}
% The following definition is copied from authortitle.bbx/authoryear.bbx
\defbibenvironment{nolabelbib}
{\booltrue{titlefirst}\list
{}
{\setlength{\leftmargin}{\bibhang}%
\setlength{\itemindent}{-\leftmargin}%
\setlength{\itemsep}{\bibitemsep}%
\setlength{\parsep}{\bibparsep}}}
{\endlist\boolfalse{titlefirst}}
{\item}
\usepackage{filecontents}
\begin{filecontents}{\jobname.bib}
@misc{A01,
author = {Author, A.},
year = {2001},
title = {Alpha},
}
@misc{B02,
author = {Buthor, B.},
year = {2002},
title = {Bravo},
}
@misc{C03,
author = {Cuthor, C.},
year = {2003},
title = {Charlie},
}
\end{filecontents}
\addbibresource{\jobname.bib}
\addbibresource{biblatex-examples.bib}
\nocite{C03,companion,worman,piccato,aristotle:physics}
% Enable sort by title
\DeclareSortingScheme{titleauthor}{
\sort{\field{sorttitle}\field{title}}
\sort{\field{author}\field{editor}\field{translator}}}
% Redefine titlefirst to be the same as the original title from biblatex.def
\newbibmacro*{titlefirst}{%
\ifboolexpr{
test {\iffieldundef{title}}
and
test {\iffieldundef{subtitle}}
}
{}
{\printtext[title]{%
\printfield[titlecase]{title}%
\setunit{\subtitlepunct}%
\printfield[titlecase]{subtitle}}%
\newunit}%
\printfield{titleaddon}}
% Each bibitem, check if we're in titlefirst env
% If so, put a title at the beginning, clear original title bibmacro
\AtEveryBibitem{
\ifbool{titlefirst}{
\renewbibmacro*{begentry}{\usebibmacro{titlefirst}\newunit}
\renewbibmacro*{title}{} % Clear original title bibmacro
}
}
\begin{document}
\noindent Some text \autocite{A01,B02}.
\printbibliography[title={References},category=cited]
\printbibliography[env=nolabelbib,sorting=titleauthor,title={Further Reading},notcategory=cited]
% Print the first bibliography again to be sure we haven't ruined
% Something permanantly
\printbibliography[title={References},category=cited]
\end{document}

BibliographyDriverfor each bib type in the style you desire. What is the base style of the second bibliography? Which types do you need (book, article...)? – cslstr May 22 '14 at 14:34