This is story related and cannot be missed. You will need three dog heads to use on a door in the Main Hall of the "Main House" level in order to move on. As you make your way through, you may or may not be able to find the dog heads on your own. If not, there's a memo in Grandma's Room (which you can open with the Scorpion Key) about where to find all of the dog heads.
The first (blue) is inside a book that can be found in the Recreation Room (on a shelf across from the VCR). You must interact with the book and open it. The second (white) involves solving the "clock puzzle" in the Living Room. The pendulum you need for the puzzle is in another clock located in the Main Hall (beside the Scorpion Door). Take the pendulum and backtrack to the first area of the house (where you were eating your lovely meal earlier). The Living Room is attached to the kitchen. Interact with this clock and put the pendulum in to get this dog head.
Finally, the third dog head comes from completing the boss fight of this level. After using the Dissection Room Key, you will make your way to a shelf with the last dog head (red) in plain sight. Unfortunately, you won't be getting it without a fight. Jack will take the dog's head away, and you must fight in order to leave with it safely. After the fight, you can now leave and backtrack to the Main Hall.
With all three in hand (or one at a time), put them in to the door in the Main Hall. As soon as you walk out the door, you will be in the "Yard" area, and the achievement will unlock.
It should be noted that the heads can be obtained in ANY order. After you fight Jack, the Main House will be 100% completely safe. You don't have to worry about sneaking around to avoid him, so if it's easier to get the other two dog heads after this point, that's also an option.