Dissipative Kerr solitons are broadband, low-noise optical-frequency combs generated using optical microresonators. They produce stable temporal pulses and demonstrate significant potential for use in spectral analysis, communications, and precision measurement. A breather soliton, which is a unique subset of dissipative Kerr solitons, is characterized by its rhythmic pulse-duration and peak-intensity oscillations. In this study, we scrutinized the dynamics of a breathing dissipative Kerr soliton within a silicon-nitride microresonator. We experimentally observed a breathing frequency of approximately 290 MHz, which shows instability in the megahertz range, thus posing a significant challenge to practical applications. Nevertheless, by applying an appropriate modulation signal to the pump laser within the fluctuation range of the breather's frequency, the breathing frequency can be injection locked to the frequency of the modulation signal, with the injection locking not exceeding 10 MHz, and the linewidth is compressed from 11 MHz to 35 kHz after locking. Additionally, we discovered another type of breather during our experiments, which was induced by intermodal interactions and had a breathing frequency of approximately 295 MHz. This breather was subjected to injection locking, which stabilized its frequency. Our study provides innovative avenues for the practical utilization of whispering gallery modes within microcavities, which are anticipated to be applied as multiwavelength sources in multichannel amplitude-modulated continuous-wave LiDAR technology.