  We present the analysis of the rest-frame optical-to-UV spectrum of APM
08279+5255, a well-known lensed broad absorption line (BAL) quasar at $z =
3.911$. The spectroscopic data are taken with the optical DOLoRes and near-IR
NICS instruments at TNG, and include the previously unexplored range between C
III] $\lambda$1910 and [O III] $\lambda\lambda$4959,5007. We investigate the
possible presence of multiple BALs by computing "balnicity" and absorption
indexes (i.e. BI, BI$_0$ and AI) for the transitions Si IV $\lambda$1400, C IV
$\lambda$1549, Al III $\lambda$1860 and Mg II $\lambda$2800. No clear evidence
for the presence of absorption features is found in addition to the already
known, prominent BAL associated to C IV, which supports a high-ionization BAL
classification for APM 08279+5255. We also study the properties of the [O III],
H$\beta$ and Mg II emission lines. We find that [O III] is intrinsically weak
($F_{\rm [OIII]}/F_{\rm H\beta} \lesssim 0.04$), as it is typically found in
luminous quasars with a strongly blueshifted C IV emission line ($\sim$2500 km
s$^{-1}$ for APM 08279+5255). We compute the single-epoch black hole mass based
on Mg II and H$\beta$ broad emission lines, finding $M_{\rm BH} = (2 \div 3)
\times 10^{10}\mu^{-1}$ M$_\odot$, with the magnification factor $\mu$ that can
vary between 4 and 100 according to CO and rest-frame UV-to-mid-IR imaging
respectively. Using a Mg II equivalent width (EW)-to-Eddington ratio relation,
the EW$_{\rm MgII} \sim 27$ \AA\ measured for APM 08279+5255 translates into an
Eddington ratio of $\sim$0.4, which is more consistent with $\mu=4$. This
magnification factor also provides a value of $M_{\rm BH}$ that is consistent
with recent reverberation-mapping measurements derived from C IV and Si IV.
