Why a nuclear-proof battleship is not practical

How could a navy build a battleship able to withstand a nuclear weapon?

It could not do so in any practical sense; even extreme lead protection would not remove the destructive effects of the explosion and would create an unusable ship.

A genuinely nuclear-proof battleship cannot be built. Surrounding the ship with an extreme amount of lead would still leave the explosion itself as a destructive problem. The weight and material required would also make the vessel impractical before it faced combat. Conventional armor logic reaches a limit where it no longer produces a viable survivability solution.