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This stage begins with Octodad at the entrance of Gervason's Grocery. For the first achievement/trophy, avoid going down the middle aisle, as this will trigger a scene in which a woman puts the last box of Sports Johnson cereal in her cart, before Octodad can grab it. Instead, start by going down the frozen food aisle and climb onto the display on the right. This should put Octodad right beside the left shelf of the middle aisle, where the cereal is located. Use Octodad's arm to reach over the shelf and grab the Sports Johnson cereal, earning the achievement/trophy.
Before going for the frozen pizza, you can find two ties: place the cubed meat on the saw at the back of the store to grind them up, after which the first tie (1/3) will appear. Then, climb up onto the shelf holding the milk. By the wall at the end of the shelf, you should see some pipes. Use them as steps to reach the bell, after which you can step onto the vent, where another tie (2/3) is sitting. Return to the frozen aisle to find only one open door, all the way at the end of the aisle. Enter through this door and squeeze Octodad along the path inside, over and between shelves. Eventually, he'll be sucked into the ventilation and down onto the other end of the aisle, allowing Octodad to pick up the box of frozen pizza.
In the produce section, you'll have to find "the perfect apple," which is the only yellow one in the batch. You can also set aside some bananas to find a yellow tie (3/3) hiding between them. For an achievement only on Xbox and Steam, grab a lemon and bring it to the cash register, where you should see a scanner. Attempt to scan the lemon by placing it on the scanner, and you should earn this easy achievement.
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For another achievement/trophy, Octodad must drop an item into every other shopper's cart. There are four shoppers in total: a woman in a blue dress, a woman in a yellow dress, a woman in a green dress, and a man in a suit. If you have trouble placing the item in the cart, stand in front of them so that they stop moving, and pick out smaller items to squeeze in between their own items, such as the sunglasses located at the front of the store (Octodad can also wear these). The last two items to pick up are mango soda and chocolate milk. For the mango soda, climb the soda display and grab it off the plane. For the chocolate milk, toss aside some cartons of regular milk to find it in the very back of the shelf.
All that remains is to grab a sushi sample in the back of the store. Proceed past the meat section, through the newly-opened doors, to find a sushi sample that Octodad can grab. Doing so will trigger a chase. Simply outrun the chef (you'll have to stop to mop the sticky floor in the middle of the chase) to survive this stage. Proceed to register and scan all of Octodad's items to checkout and complete the stage.