The interplay of charge, spin, orbital and lattice degrees of freedom has recently received great interest due to its potential to improve the magnetocaloric effect (MCE) for the purpose of magnetic cooling applications. Here, a new mechanism for a large entropy change with low magnetic fields in rare-earth tetraborides, especially for Ho1-xDyxB4 (x=0.0, 0.5, and 1.0), is proposed. For x=0.0, 0.5, and 1.0, the maximum entropy changes of the giant inverse MCE are found to be 22.7J/kgK, 19.6J/kgK, and 19.0J/kgK with critical fields of 25kOe, 40kOe, and 50kOe, respectively. For all compounds, systematic study on how the entropy changes as a function of the field and temperature is performed to investigate their correlation with consecutive double transitions, i.e., the magnetic dipolar order at T=T-N and the quadrupolar order at T=T-Q (T-Q<T-N). Based on Landau theory, it is found that this behaviour is attributed to the strong coupling between magnetic dipoles and quadrupoles in the presence of strong spin-orbit coupling and geometric frustration. Our work offers new insights into both academic and industrial interests in the discovery of giant MCE with various applications for magnetic cooling systems.