Collective behaviour in biological systems often emerges from the interactions of individual agents, such as migrating cells during development, or pigment cells underlying zebrafish skin pattern formation. Agent-based models provide a flexible framework for capturing these processes. However, inferring the parameters in such models poses significant challenges that limit the predictive power of these models. We demonstrate that combining topological data analysis with an approximate Bayesian inference framework offers a computationally tractable approach to inferring parameters governing cell migration and cell-level interactions. In our study, we focus on an existing agent-based model of pattern formation in zebrafish skin, and show the proposed approaches is capable of providing accurate estimates of model parameters in this complex, stochastic model. We also discuss how various choices in the analysis pipeline affects the accuracy of parameter estimates, and how to use posterior predictive check to appropriately tune hyper-parameters.