The Difficulty Achievements Do Not Stack
You must play the Sega (S) Version of the game.
You CANNOT use Watch Mode for the Easy and Hard Difficulties. (Watch mode uses Normal Difficulty by Default)
However, you CAN use the old Sega Genesis Cheats to Automatically beat a level. To Use Cheats: Press Pause/Start during the same
-Start Up The (S) Version
-Change Difficulty to "Practice"
-Start your game
-Simply input the Cheat until you Beat all the Levels
Here is my Video Guide for The Aladdin Achievements: