This is a relatively easy achievement. Might take you some time but overall not hard.
Achievement's OFFICIAL description is incorrect though. To unlock this achievement you have to play through the ENTIRE game from "Mansion" through to "Ice" (including the Mansion stage covered in snow after the "Ice" level.
So just sit back, enjoy yourself and just run through the entire game in one sitting. Restarting last checkpoint will not void the achievement. I was going for all the other achievements when doing this and messed up a couple of times and had to restart from last checkpoint.