This paper investigates the natural frequencies and vibration modes of launch vehicle fuel tanks, modeled as compartmentalized shell structures containing liquids at varying fill levels. The primary goal is to develop robust methods for analyzing the dynamic behavior of thin-walled aerospace structures, accounting for factors such as elasticity, hydro-elastic interactions, and liquid sloshing within compartments. A comprehensive formulation addresses the hydro-elastic vibration problem in shells partially filled with an incompressible, ideal fluid. Each compartment contains liquid that may exhibit distinct properties and varying filling levels over time. Coupled finite and boundary element methods are used for numerical simulations, with test cases on spherical and conical shells. Results are validated against established numerical and analytical findings, covering both empty and liquid-filled configurations. Key findings include the identification of sloshing frequencies and modes, their dependency on variable gravitational conditions, and the free vibration frequencies of the liquid-filled elastic structure. For the first time, this work provides frequency and mode analyses of a shell structure with two partially filled compartments, integrating effects from wall elasticity, liquid sloshing, varying gravitational influences, and different fill levels. The study also explores the impact of varying load levels across different stages of mission, offering new insights into the vibration characteristics of launch vehicle fuel tanks under realistic operational conditions.