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 pseudocubic 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 with the cubic to tetragonal phase transition at Tc ≈ 230 K. Low frequency and highly damped optical phonons observed using both Raman and inelastic neutron below 18 meV, do not present softening close to Tc. The critical dynamics at Tc ≈ 230 K is compatible with an order-disorder character, dominated by relaxational motions of the molecules.