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] $lambdalambda$4959,5007. We investigate the possible presence of multiple BALs by computing balnicity and absorption indexes (i.e. BI, BI$_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 ($F_{rm [OIII]}/F_{rm Hbeta} lesssim 0.04$), 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.
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