The author deals with Painlevé equations P\(_J\), \(J=\text{I,\dots,VI}\), with a large parameter \(\eta,\) each of which is represented in the form of a Hamiltonian system \[ d\lambda/dt=\eta\partial K_J/\partial\nu, \quad d\nu/dt=-\eta\partial K_J/\partial\lambda. \tag{1} \] By the localization at a \(0\)-parameter solution \[ \lambda=\lambda^{(0)}_J(t)+\eta^{-1/2}U, \quad \nu=\nu^{(0)}_J(t)+\eta^{-1/2}V, \] system (1) is changed into \[ dU/dt=\eta \partial \mathcal K_J/\partial V, \quad dV/dt=-\eta \partial \mathcal K_j/\partial U. \tag{2} \] The author constructs a formal canonical transformation \((U,V)\mapsto (\widetilde{U},\widetilde{V})\) of the form \[ \begin{aligned} & U=u_0(\widetilde{U},\widetilde{V})+\eta^{-1/2}u_1 (\widetilde{U},\widetilde{V})+\cdots, \\ & V=v_0(\widetilde{U},\widetilde{V})+\eta^{-1/2}v_1 (\widetilde{U},\widetilde{V})+\cdots, \end{aligned} \] that reduces (2) to its Birkhoff normal form, and obtains instanton-type formal solutions. Furthermore, for a system with a polynomial Hamiltonian \(H_{\text{VI}},\) he examines local properties of its Birkhoff normal form around a regular singular point \(t=0;\) it is shown that each coefficient has a simple pole at \(t=0,\) and its residue is computed.