Due to the electronic bottleneck limited real-time measurement speed of common temporal-spectral detection and the particle-like nature of optical soliton enabled nonrepeatable transient behaviors, capturing the ultrafast laser pulses with unknown times of arrival and synchronously characterizing their temporal-spectral dynamic evolution is still a challenge. Here, using the Raman soliton frequency shift based temporal magnifier and dispersive Fourier transform based spectral analyzer, we demonstrate a self-synchronized, ultrafast temporal-spectral characterization system with a resolution of 160 fs and 0.05 nm, and a recording length above milliseconds. The synchronized nonlinear process makes it possible to image full-filled temporal sub-picosecond pulse trains regardless of their arrival times and without extra pump lasers and photoelectric conversion devices. To demonstrate the significance of this improvement, a buildup dynamic process of a soliton laser with a complex breakup and collisions of multisolitons is visually displayed in the spectral and temporal domains. The soliton dynamic evolution processes observed by our characterization system are in one-to-one correspondence with the numerical simulation results. We believe this work provides a new multidimensional technique to break the electronic bottleneck to gain additional insight into the dynamics of ultrafast lasers and nonlinear science.