This achievement is unmissable, as it is necessary in the story.
*** Spoiler - click to reveal ***In the past, find the bucket, brush and soap and wash the carriage outside.
For the bucket and brush, go through the swinging door in the Founding Fathers room into the kitchen, and then to the right. There is the bucket, and the brush is in the red cupboard.
Go back one room and use the bucket with the water pump.
Then go upstairs.
In George Washington's room (the first room after you get up the stairs), push his bed to make it messy. Then pull the cord on the left to call in the maid.
While the maid is cleaning, go out, and in the cart you'll find the soap.
Add the soap to the bucket of water.
Go outside to the dirty carriage. Use the brush on the carriage to wash it.