To reach this hidden area, you will need to have obtained Risky's Boots.
Return to Saliva Island and head straight for the lower dungeon area (the one unlocked when Shantae accidentally stonified the man to open it).
As soon as you drop in you need to walk to the right side of the room and then Charge to the left to break through into an area that uses background tiles more like the classic Game Boy Shantae game.
The Achievement unlocks merely by entering the area. If you complete the area, you exit back into the same room you had entered from.