The widely used Pseudo-Two-Dimensional (P2D) cell model for Li-ion batteries is generally based on a simplified lithium diffusion model of active particles with certain geometry. In this work, we propose a two-level framework, which extends the P2D cell model and incorporates a mechanically coupled phase-field Cahn-Hilliard diffusion model of active particles. The phase-field model allows more detailed diffusion study in particles of general geometry and includes the full coupling of the mechanics and phase separation. To improve the computational efficiency, we manage to reduce one degree of freedom at the cell level by treating the ion flux between the electrolyte and active particle as a dependent quantity. The two-level framework is validated against the original one and applied to study the impact of particle geometry, finite deformation elasticity and phase separation on the cell performance. Results show that the oblate particle has better cell performance than other spheroidal particles. It is attributed to the mechanical drifting at the higher curvature.