To build the Prestihatinator you will need four rabbits, four boards, and one top hat. I don't know if it's a smart thing to rush the build of this since it's resources could take a bit of time to gather, and honestly, you should be establishing your base so you don't starve before you decide to build it. But I'll give a few tips that helped me eventually get enough resources to build it without taking too much time from my necessary tasks.
You will need a science machine to get the recipe to craft this, so yeah needless to say play the game as you normally would to the point of trying to establish a base with a science machine, and once you have a good amount of food you can focus on getting the individual resources for the item. Shouldn't take more than a few days to gather everything if you focus on them after you've established a simple base.
The boards are the easiest part of the recipe to obtain since all you have to do is chop down a bunch of trees. One board equals four logs, so that's sixteen logs total (you can hold up to 20 in a stack in your inventory). Chopping down trees is a necessity in Don't Starve, so I suggest spending at least one to two full days chopping down as much wood as you can. You should have enough wood to make a chest as well, and I suggest storing the four boards away in there until you are ready to craft. You could even get the Treeguard achievement during this, as it will appear to attack you if you chop down too many trees. Plant some pinecones around you if it gets near, and that'll stop it from attacking you.
To make a Top Hat you need six silk, which you obtain from killing spiders. Once you find a nest, the easiest thing to do is bring 2-3 traps with you, and when you get near the nest let the spiders chase you. Drop your traps as you run away and the spiders will run right into them. Once you pick up the trap with the spider in it, you will receive either monster meat, a spider gland, or silk. In my experience silk was always the least likely to appear, but just keep coming back to the nest every few minutes and eventually, you'll get enough. You might get lucky and find a bunch of spider nests near each other, which will make things go faster. You can also kill the spiders, but if it's early days I would suggest avoiding fighting until you have decent armor and weapons.
Once you have the Top Hat and boards, focus on getting the rabbits. You probably already know how to get rabbits: baiting them into traps, leaving traps on top of their holes for when they enter/exit in the morning/evening, shoveling the holes with a trap next to it for them to run into, etc. Save the rabbits for last, as you don't want them to starve and turn into morsels before you have enough time to gather the rest of the supplies. If your sanity is low, the rabbits will become beardlings, but that's ok as you can still craft the Prestihatinator with them.
I hope these tips help; there are so many different playstyles for this game and honestly you should not rush to build it for the sake of the achievement, but rather work towards establishing yourself and protecting yourself from the harsh world, and taking a few minutes each day (in-game) to gather the necessary supplies for the Prestihatinator.