This paper examines the identification of the parameters of the Doyle-Fuller-Newman electrochemistry-based Lithium-ion battery model from voltage and current cycling data. The battery used in this study has a lithium iron phosphate cathode chemistry intended for high-power applications such as plug-in hybrid electric vehicles. The variables optimized for model identification include parameterizations of the model's anode equilibrium potential, cathode equilibrium potential, and solution conductivity. A genetic algorithm is used to optimize these model parameters against experimental data. The resulting identified model fits two experimental data sets used for system identification, as well as separate validation data sets corresponding to five different vehicle drive cycles. These drive cycles simulate the current a battery would undergo while used in a plug-in hybrid vehicle battery pack. The accuracy of the parameters is investigated using various validation data sets. This is believed to be the first attempt at fitting nearly all of the parameters and functions in the DFN model simultaneously using only voltage and current data. Computational logistics of using a genetic algorithm to identify 88 parameters of an electrochemistry-based model for 7.5 hours of cycling data are discussed. In addition, a detailed analysis of local parameter identifiability is presented.