Start game on Easy and play until you have gotten past the first Djin. Upgrade at least 2 things to the next level. Now, start a new game on Normal. When the game starts, switch the difficulty to Easy and then follow the story till the first Djin again. Just after that area you will see that you upgrades from the last game will appear and all the XP in the levels have been reset (Monsters and Sarcophagi). Do this as many times you like and you can have all the available upgrades; and you can save up upgrade points for the later unlocked ones.

Start a new game after defeating the final Boss and immediately open up the upgrade menu -- all your old upgrades will still be there but won’t come into effect until the sand army is released (when you can first start upgrading your prince). With this information you should be able to go back through and get anything you may have missed first time round.