  For regular $SU(3)$ Toda systems defined on Riemann surface, we initiate the
study of bubbling solutions if parameters $(\rho_1^k,\rho_2^k)$ are both
tending to critical positions: $(\rho_1^k,\rho_2^k)\to (4\pi, 4\pi N)$ or
$(4\pi N, 4\pi)$ ($N>0$ is an integer). We prove that there are at most three
formations of bubbling profiles, and for each formation we identify leading
terms of $\rho_1^k-4\pi$ and $\rho_2^k-4\pi N$, locations of blowup points and
comparison of bubbling heights with sharp precision. The results of this
article will be used as substantial tools for a number of degree counting
theorems, critical point at infinity theory in the future.
