The first search for $K_L^0 \rightarrow \pi^0 e^+e^-e^+e^-$ is performed with a dataset collected by the J-PARC KOTO experiment in 2021. In the dark sector model, this final state can be achieved through $K_L^0 \rightarrow \pi^0 X X,$ where $X\rightarrow e^+e^-$ [1]. The branching ratio of this decay mode is predicted to be $\mathcal{O}$($10^{-10}$) dominated by the virtual photon vertex through $K_L^0\rightarrow \pi^0 \gamma^* \gamma^*$ in the Standard Model. With the data collected in 2021, we can achieve a sensitivity close to this level which can improve the constraints on the dark sector model. Special analysis methods are used for the rejection of backgrounds related to the $\pi^0$ Dalitz decay. The result of the analysis based on data taken in 2021 will be discussed.