Curd of the Ancients

For this method, the first thing you need to do is gain control of a medium sized doll with a violin.
Take her to the Pied Piper, who is located on the side opposite of the exhibit.
Play your violin in front of the Piper to get him to come down, allowing you to stack into him.
Head up the stairs to the second floor of the ship and follow the path around to the side of the cafeteria. There should be some trash with a bunch of rats nearby.
Use the Piper's song to lead the rats to the exhibit, where they will proceed to feast upon the cheese statue.

Mummy Dearest

Head into the exhibit and look along the left wall to find a guard and a bunch of kids near him.
Take control of the guard and use his ability to pick up small dolls and place them somewhere else. Doing so will clear the path to the mummy doll.
Stack out of the guard and into the mummy doll and then simply waltz right on out the door.

Queen of Argyle

Just outside the museum is the tallest of the illusionist family. Take control of him and work your way into the museum.
Use his ability on the Queen's Statue — The one in front of the purple background — to cause it to blend in with the background, leaving people to believe that it is missing.

Relic Rustler

Stack into a variety of dolls inside the exhibit until you're large enough to stack into the gilded sarcophagus in the box at the back.
Use its ability to draw a crowd. The one you want to get the attention of is the large lady with the hat. When she turns around, stack into her and then walk on outside.

The Fighting Pharaoh

Take control of the strong armed doll once again and lead him into the exhibit.
Perform a proper uppercut on the small pharaoh head in the middle of the exhibit.