He starts to look like a cunning, fox-like prime minister who exploits his power to the fullest for his own self-preservation.
Literal
Maximum [to-に] prime-minister [called-という] power [object-を] exploit, self [possessive-の] self-preservation [purpose-の為に] exploit fox [like-のように] sly prime-minister [to-に] appear-come.
キツネのようにずる賢い 'cunning like a fox' — a cross-culturally understood metaphor. 保身 'self-preservation/self-protection.' 見えてくる uses the auxiliary ~てくる to mark a gradual emergence: 'starts to appear, comes to look like.' The long relative clause piles up criticisms before the head noun 首相.