For this Achievement you need to collect every penny from all areas of the museum.

All credit goes to YouStayCla55y

New York Museum of Natural History

Locations:
Quarter #1 - From where you start walk straight ahead to where there's a staircase on either side. Take the stairs on the right and climb up the giant stack of crates
Quarter #2 - While riding Roxy take a right and go to entrance to museum. It's hanging right above it
Quarter #3 - While riding Roxy take a left and go to where there's a staircase on either side. It's hanging above between them
Quarter #4 - While riding Roxy go into hallway on left side of first floor. Break all the crates by walking over them, it's in a crate in the middle of the hallway
Penny - In the Egpyt room, use your keychain to break the vase in the corner. It's inside

Smithsonian Castle

Locations:
Quarter #1 - From where you start take a left and follow the tiny hallway
Penny - From where you start, enter next room and walk directly to right. It's in a corner
Quarter #2 - From where you start, enter next room and walk directly right into the next room with the giant stone head. It's on the far right side
Quarter #3 - From where you start, enter next room and walk directly to the left into the next room with Egpytian sarcophagus. Walk left into the next room, it's right inside
Quarter #4 - Inside security room to the left

Lincoln Memorial

Locations:
Quarter #1 - From where you start, walk directly to the left
Quarter #2 - On the far right side as you walk up the stairs after the lightning pole
Quarter #3 - On the far left side against the wall at the top of the stairs
Penny - Lower left hand corner inside Lincoln Memorial
Quarter #4 - Far right side inside Lincoln Memorial

Federal Archives

Locations:
Quarter #1 - Walk down stairs and take a left
Penny - After Quarter #1 keep walking straight
Quarter #2 - After Penny climb on top of crates ahead
Quarter #3 - Opposite corner of the room from the Amelia Earhart display
Quarter #4 - In the center of the storage room is a tower of crates with Dexter the monkey holding the Tablet on top. Halfway up, walk around the crates to find the quarter

National Air and Space Museum

Locations:
Quarter #1 - From where you start walk to far left corner of room and turn around to see quarter
Quarter #2 - Walk straight ahead after the cut scene where you free Able
Penny - Walk to far left of room and behind the Space Station 3D theatre display
Quarter #3 - After passing the launch blasters, walk straight ahead to the corner to get quarter
Quarter #4 - At bottom of stairs after the rocket blasters, take a sharp right to pick it up

Washington Art Museum

Locations:
Quarter #1 - Falls out of one of the broken paintings you fix in Cherub room
Quarters #2 & #3 - Both fall out of broken paintings you fix in the small Key Painting room
Quarter #4 - Falls out of one of the broken paintings you fix in Thinker room
Penny - Falls out of the first broken painting you fix after you escape the Cage rooms

National Museum of Natural History

Locations:
Quarter #1 - From where you start walk to the left
Quarter #2 - Jump onto the pteryodactly, it's right on top
Quarter #3 - On the lower level rotunda, right across from the Egyptian display
Quarter #4 - On the upper level rotunda, atop the glass case closest to the rhino. You will need the Animal Power to tame the rhino before you can grapple up to get it
Penny - Inside the gate on the far right side of the room in the icy area, you need Animal Power to make the rhino knock the gate down.