Abstract: Integrated Sensing and Communication （ISAC） technology has emerged as a new paradigm for beamforming （BF） optimization in highly dynamic Flying Ad-Hoc Networks （FANET）， owing to its spectral efficiency， low energy consumption， and cost-effectiveness. Herein， an energy-efficient Intelligent Reflecting Surface-Aided Antenna （IRS-A） is introduced into the clustered architecture of FANET. By jointly optimizing the ISAC transmit and receive BF at the Cluster Head （CH） and the communication receive BF at the sensing-targeted Cluster Member （CM）， we enhance the sensing performance of CH-CM links in FANET-ISAC systems. Specifically， sensing mutual information （SMI）， defined as the conditional mutual information between target response channels and echo signals， is adopted to characterize the theoretical limit of information acquisition for sensing targets. An optimization framework is established with SMI as the performance metric under constraints of transmission power budgets， IRS-A phase shifts， and communication quality-of-service requirements. To address this complex non-convex problem with coupled variables， a hybrid CH-CM BF alternating optimization algorithm is proposed. The original problem is sequentially decomposed into subproblems and solved iteratively： the receive digital BF at the CM is acquired based on the Rayleigh theorem， the CH ISAC transceiver BF subproblem is reformulated through the alternating direction method of multipliers， the closed-form solutions are derived using the weighted minimum mean-square error， and IRS-A phase shifts are optimized via manifold optimization. Simulation results demonstrate that the proposed algorithm significantly improves the SMI and sensing energy efficiency of FANET-ISAC systems.