Most games give you the Achievement Points that you earned while playing the demo if you purchase the game. In fact, the majority of them actually taunt you with them. Not Shrek-n-Roll.
I played through the demo levels, which is three in total I believe, payed for the game, and completed the first full level, getting the "Top of the Class" Achievement for clearing Worchestershire Academy.
The problem is that there is a 5 point Achievement "Get Your Feet Wet" for clearing just the first board. It would not give this to me, even if I started a new game.
I deleted the game, that did not work. I tried on another profile, which worked just fine. So the solution is to go into the System Blade, Memory, Games, Shrek-n-Roll and delete the save file (it will have your Gamertag) and start the game again. Then, you will get the "Get Your Feet Wet" Achievement.
I know I am getting flack for this, but its a fun little puzzle game. In fact, I cannot think of another dual-analog puzzler, at least not like this one.