In the field of long-wave infrared (LWIR) thermal imaging, vital for applications such as military surveillance and medical diagnostics, metalenses show immense potential for compact, lightweight, and low-power optical systems. However, to date, the development of LWIR broadband achromatic metalenses with dynamic tunable focus, which are suitable for both coaxial and off-axis applications, remains a largely unexplored area. Herein, we have developed an extensive database of broadband achromatic all-As2Se3 microstructure units for the LWIR range. Utilizing this database with the Particle Swarm Optimization (PSO) algorithm, we have designed and demonstrated LWIR broadband achromatic metalenses capable of coaxial and off-axis focusing with three dynamic tunable states. This research may have potential applications for the design of compact, high-performance optical devices, including those with extreme depth-of-field and wide-angle imaging capabilities.