The hybrid solid-state DC circuit breakers (DC CBs) have become one of the most promising technologies to address the protection challenges within multi-terminal DC (MTDC) grids. Those breakers are designed in such a way that a large number of identical modules are connected in series to enable extinguishing the fault current with the arresters embedded in them. Conventionally, these modules are commanded to trip simultaneously, creating significant overvoltage and overcurrent stresses for the rest of the system. To attenuate these adverse impacts, in this paper, a sequential tripping method is proposed to improve the performance of hybrid DC CBs through commanding the main breakers to trip in a sequential manner. It has been verified that by the proposed method, fault clearance is expedited while the maximum overcurrent is reduced. To address the unbalanced energy absorptions among the different modules of the CB, a modified sequential tripping scheme is also proposed. By rescheduling the sequential tripping sequence, this method enables an equal redistribution of energy, which greatly reduces the risk of thermal overloading. Both of the proposed methods are evaluated and tested under a practical six-terminal DC grid in the PSCAD/EMTDC software environment. The performance and effectiveness of the proposed methods are confirmed by simulation results.