Performing highly agile acrobatic motions with a long flight phase requires perfect timing, high accuracy, and coordination of the full-body motion. To address these challenges, we present a novel approach on timings and trajectory optimization framework for legged robots performing aggressive 3D jumping. In our method, we firstly utilize an effective optimization framework using simplified rigid body dynamics to solve for contact timings and a reference trajectory of the robot body. The solution of this module is then used to formulate a full-body trajectory optimization based on the full nonlinear dynamics of the robot. This combination allows us to effectively optimize for contact timings while ensuring that the jumping trajectory can be effectively realized in the robot hardware. We first validate the efficiency of the proposed framework on the A1 robot model for various 3D jumping tasks such as double-backflips off the high altitude of 2m. Experimental validation was then successfully conducted for various aggressive 3D jumping motions such as diagonal jumps, barrel roll, and double barrel roll from a box of heights 0.4m and 0.9m, respectively.