We establish results concerning the approximate controllability for time-dependent impulsive neutral stochastic partial differential equations with memory in Hilbert spaces. By using semi group theory, stochastic analysis techniques and fixed point approach, we derive a new set of sufficient conditions for the approximate controllability of nonlinear stochastic system under the assumption that the corresponding linear system is approximately controllable. Further, the above results are generalized to cover a class of much more general impulsive neutral stochastic delay partial differential equations driven by Lévy noise in infinite dimensions. Finally, an example is provided to illustrate our results.