Among of the wide range of potentially interesting astrophysical sources for gravitational wave detectors Advanced LIGO and Advanced Virgo are galactic core-collapse supernovae. Although detectable core-collapse supernovae have a low expected rate (a few per century, or less) these signals would yield a wealth of new physics. Of particular interest is the insight into the explosion mechanism driving core-collapse supernovae that can be gleaned from the reconstructed gravitational wave signal. A well-reconstructed waveform will allow us to assess the likelihood of different explosion models, perform model selection, and potentially map unexpected features to new physics. This dissertation presents a series of studies evaluating the current performance of burst parameter estimation algorithms in reconstructing core-collapse supernovae gravitational wave signals in both simple Gaussian noise and realistic non-Gaussian detector noise. The introduction of non-Gaussian noise has a significant impact on the recovery of core-collapse supernova models from the data. Terrestrial noise is also an important factor in the recovery of any gravitational wave search. This work also details a series of studies that enable the characterization of ground motion local to the Advanced LIGO inteferometers and the ability of the installed active seismic isolation to mitigate it.