We consider a priori estimates of the Weyl's embedding problem of $(\mathbb{S}^2, g)$ in a general $3$-dimensional Riemannian manifold $(N^3, \bar g)$. We establish the mean curvature estimate under natural geometric assumptions. Together with a recent work by Li-Wang, we obtain an isometric embedding of $(\mathbb{S}^2,g)$ in Riemannian manifolds. In addition, we reprove Weyl's isometric embedding theorem in space forms under the condition that $g\in C^2$ with $D^2g$ Dini continuous.