Low frequency dynamics has been studied in a CH3NH3PbBr3 hybrid perovskite single crystal, by using four different spectroscopy techniques: coherent inelastic neutron, Raman and Brillouin scatterings and ultrasound measurements. Sound velocities were measured over five decades in energy to yield the complete set of elastic constants in a hybrid halide perovskite crystal in the pseudo cubic plastic phase. The C44 shear elastic constant is very small, leading to a particularly low resistance to shear stress. Brillouin scattering has been used to study the relaxation dynamics of methylammonium cations and to evidence translation-rotation coupling associated to the cubic to tetragonal phase transition at Tc≈230K. Low frequency and highly damped optical phonons observed using both Raman and inelastic neutron below 18meV, do not present softening close to Tc. The critical dynamics at Tc≈230K is compatible with an order-disorder character, dominated by relaxational motions of the molecules.