How to activate the Grandmapocalypse

Dungeons are a work in progress feature and are normally only available in the beta version of Cookie Clicker. However, it's still possible to earn these achievements in the regular game. Here are a few ways to get it, ranking from least dishonest to most dishonest:

Earn the achievements in the beta and import them

Because newer version of cookie clicker can import saves coming from older versions, if you play the beta and earn the achievements there, you can import that save into the regular game and you will have the achievements.

To earn the achievements, you'll need to unlock the factory dungeons first. This requires 50 factories. Once you attain that number, the dungeons will be unlocked automatically. Click on "Enter dungeons" and you'll be granted access to the dungeons. Click the arrow keys to control your hero, whose stats depend on your CPS.

The first two should be easy, as the Sentient Furnace and the Ascended Baking Pod are bosses which appear on every level. The other two will be trickier since they are rare and will appear randomly based on chance. Remember to explore all the rooms as there's a better chance of them appearing the deeper you go into a level.

I suggest you enable auto-explore (enter Game.Objects.Factory.dungeon.auto = 1 on the console if it's not set to auto-explore already) and leave the game running.

Unlock the dungeons in the live version

If you have made significant progress in your game, you might not want to lose all your progress. Luckily, you can unlock the dungeons in the regular version of cookie clicker. There are a few ways to do this. The easiest way is to open the Console (F12 on Chrome or Ctrl+Shift+K on Firefox; varies from browser to browser) and enter the following command:

Game.Objects.Factory.unlockSpecial()

Once the dungeons are unlocked, you can earn them like you would in the beta.

Cheat the achievements in

Simply open the console and give yourself the achievements by entering the following commands:

Game.Win('Getting even with the oven');
Game.Win('Now this is pod-smashing');
Game.Win('Chirped out');
Game.Win('Follow the white rabbit');

This won't give you the "Cheated cookies taste awful" achievement.

(Yes, note the Christmas Hat)

Wrinklers are leech-like creatures which has a 0.0003% chance to spawn, per frame, and the chances increase as you go through each stage of the Grandmapocalypse.

When spawned, they will appear in the Big Cookie Window, where it'll move towards your cookie.

When a Wrinkler is attached to your cookie, you gain a 5% debuff to your Cookie Per Second, and this stacks as multiple Wrinklers attaches to it (up to a maximum of 10, thus 50% debuff).
To remove one, simply click on it (multiple times) and they'll pop, returning 1.1 times the cookies it leeched.

In the long run, although they appear to be a debuff - They actually return more than lost, since none of the cookies they leech are actually destroyed.