  We investigate the blow-up dynamics for the $L^2$ critical two-dimensional
Zakharov-Kuznetsov equation \begin{equation*} \begin{cases} \partial_t
u+\partial_{x_1} (\Delta u+u^3)=0, \mbox{ } x=(x_1,x_2)\in \mathbb{R}^2, \mbox{
} t \in \mathbb{R}\\ u(0,x_1,x_2)=u_0(x_1,x_2)\in H^1(\mathbb{R}^2),
\end{cases} \end{equation*} with initial data $u_0$ slightly exceeding the mass
of the ground state $Q$. Employing methodologies analogous to the
Martel-Merle-Raphael blow-up theory for $L^2$ critical equations, more
precisely for the critical NLS equation and the quintic generalized Korteweg-de
Vries equation, we categorize the solution behaviors into three outcomes:
asymptotic stability, finite-time blow-up, or divergence from the soliton's
vicinity. The construction of the blow-up solution involves the bubbling of the
solitary wave which ensures the universal behavior and stability of the
blow-up.
