There are two Sword upgrades in the game which will improve the strength of the attacks. These can be found at the following levels.

Formosa - Temple Of Terror:
In the second area of the level look on the left side of the narrow hallway where the enemies burst through the paper walls for the treasure chest.

Rum Island - Sand, Sky, Rum and Gold:
When the man-eating plants appear go to the right of the area where the plants first attack and find a small alcove blocked by vines which if you cut away will reveal the treasure chest.