This game is one of those games that you'll have trouble completing without a walkthrough, but also requires some brainpower on your part. A few of the achievements in particular are impossible without a walkthrough-- notably, one of them requires you to create noises with animals in a particular order that's only revealed if you've played another game by the same author.
As for my recommendation to make a piece of paper, you'll need to write down all your solutions as you figure them out and place them on a hand-drawn map. This is the fastest, most effective way to speedrun the game-- the game requires full completion within an hour for one of the achievements and not looking at the map for another achievement, and it's best to get them both at once. If you don't have photographic memory, this sort of accomplishment is impossible without a printer or a pencil-- you'll be clocking in at 45 minutes even with a full guide.