Here is an explanation of how to complete each challenge in Challenges mode, earning you the achievement “Champion of the House!”
This guide is referring the the “Challenges” mode that you can access through the main menu.
It took me a second to figure these out, so I thought I would share. Thanks for reading!

Clean Toys
Objective: Put away the baby’s toys

Instruction: Pick up the toys and place them into the toybox.
The toys include: Small wooden blocks, big colored blocks, the ball, and the toy piano.
Clean the Pool
Objective: Remove foreign objects from the pool

Instruction: Jump on in, and grab and toss out the four balls.
Pick up the Poop
Objective: Throw away the kitchen poops

Instruction: Select each poop and drag them to the trash can, where they will disappear on impact.
There are 14 poops hidden, all within the kitchen.
They are located:

In the fruit bowl
In front of the fridge
In the freezer
Inside of the kitchen island (the cabinet below the fruit bowl)
The pull-out drawer to the left of the stove
Inside of the stove
Inside of the microwave
On the kitchen counter, to the right of the stove
On top of all of the cabinets, in the corner
Inside the cabinet above the stacked glasses
In the sink
In the cabinet below the sink
On a dining chair
In the corner behind the dining table (by the sliding glass door)