Magnetars are neutron stars with an extreme magnetic field and sometimes manifest as soft gamma-ray repeaters (SGRs). SGR J1935+2154 is one of the most prolific bursters and the first confirmed source of a fast radio burst (FRB; i.e., FRB 200428). Encouraged by the discovery of the first X-ray counterpart of FRBs, the Insight-Hard X-ray Modulation Telescope (Insight-HXMT) implemented a dedicated 33-day-long Target of Opportunity observation of SGR J1935+2154 since 2020 April 28. With the HE, ME, and LE telescopes, Insight-HXMT provides a thorough monitoring of burst activity evolution of SGR J1935+2154, in a very broad energy range (1–250 keV) with high temporal resolution and high sensitivity, resulting in a unique valuable data set for detailed studies of SGR J1935+2154. In this work, we conduct a comprehensive analysis of this observation, including detailed burst search, identification, and temporal analyses. After carefully removing false triggers, we find a total of 75 bursts from SGR J1935+2154, out of which 70 are single pulsed. The maximum burst rate is about 56 bursts day−1. Both the burst duration and the waiting time between two successive bursts follow lognormal distributions, consistent with previous studies. We also find that bursts with longer duration (some are multipulsed) tend to occur during the period with relatively high burst rate. There is no correlation between the waiting time and the fluence or duration of either the former or latter burst. It also seems that there is no correlation between burst duration and hardness ratio, in contrast to some previous reports. In addition, we do not find any X-ray burst associated with any reported radio bursts except for FRB 200428.