Play up until the first time you are able to pick your classes, and pick sleep for all of them. You should get a knock on the door from Grabiner. He gives you 10 demerits, a detention, and of course, the "Truant" achievement. Simple.

It's recently come to my attention that what I originally wrote for this part wouldn't work. Thanks Kazekind for letting me know. His solution should work though:

I wasn't able to get the expulsion achievement that way. I had to earn -50 demerits (it does say expelled by earning demerits in the achievement after all). It's not too hard though. After the first week of sleeping, attend at least one magic class. Then, one can simply study until you get a visit and can choose not to get a detention for -10, and at the test, use green magic for another -10 and then study until you allow a prank to be played, and then when the teacher shows up, if you choose "run away", that's the last -10 for expulsion.

Or alternatively, after sleeping the first week, you could just give up in every dungeon until you have -50 demerits.