We present the results from thirteen years of optically monitoring the gravitationally lensed z_QSO_= 1.693 quasar HE 0435-1223. The R-band light curves of the four individual images of the quasar were obtained using deconvolution photometry for a total of 876 epochs. Several sharp quasar variability features strongly constrain the time delays between the quasar images. Using two different numerical techniques, we measured these delays for all possible pairs of quasar images while always processing the four light curves simultaneously. For both methods, the delays are compatible with the previous measurements presented in Courbin et al. (2011, Cat. J/A+A/536/A53) that used a subset of the present data and a different curve-shifting method. Our analysis of random and systematic errors accounts in a realistic way for the observed quasar variability, fluctuating microlensing magnification over a broad range of temporal scales, noise properties, and seasonal gaps. Finally, we find that our time-delay measurement methods yield compatible results when applied to subsets of the data.