Titanic

Titanic (also known as Titanic 2005) is an unlicensed Famicom game made by Nice Code/Dragon Co. and published by Shenzhen Nanjing Technology in 2005.

It can also be found on certain plug & play systems, under a different name.
Overview

In Titanic, you can choose to play as Jack or Rose, and your objective is to escape the ship. The game uses the same (or similar) gameplay engine as Dragon Co.’s other platformers, although the game does control somewhat differently. You can climb up ledges by pressing up like in Prince of Persia and the B button now just makes you run faster instead of using a weapon.

(From BootlegGames Wiki)