While solving the Mechanical Age puzzle, you will find yourself rotating the entire fortress using a set of controls atop the age's elevator (while at the highest level, push the middle elevator button, shaped like a minus sign, then hop out before the lift descends.) To solve the puzzle correctly, you need to rotate the large gear mechanism in front of you (and thus the fortress) 90 degrees clockwise from the start, then 180 degrees from start, and then return the fortress to the original position (360 degrees from start.)
To see the skeleton, rotate the fortress 270 degrees (3/4 of a unit circle) from the original position, or just 90 degrees from the second Myst book puzzle solution. Timing for this is subjective since the left lever adjusts the rotational speed, so instead go by angle. It helps that the fortress will only settle on one of the four previously mentioned positions so if you're not precise, the mechanism will move forward or backwards to the nearest stopping point.
Go down the elevator and go into Sirrus' bedroom. It is the more foppish of the two bedrooms with a toy bird and, more importantly, a telescope. You should see a skeleton image in the telescope's viewfinder and the achievement will pop without you interacting with anything in the room.
Note: some have commented on the achievement not popping for them. I had it unlock on my first try, but to be safe, make a manual save before attempting this. I attempted this while going through a random run and I do not know if it is affected by completing the good white page ending or not.
And yes I know that the fortress rotates anticlockwise, however the gear mechanism you control rotates clockwise.
EDIT: Browsing online forums, no one seems to have found a cause for the achievement not unlocking. Folks having continued issues might consider reaching out to the publisher on this. For myself, I had already beaten the game once, then started a new random game. I completed the Selenetic Age first, grabbing both colored pages in the age. I then traveled to the Mechanical Age, rotated the fortress around to 90 then 180 degrees in order to solve the Myst age linking book puzzle. I also grabbed the red and blue pages in the age. Then, before going back to Myst, I rotated the fortress to the 270 degree position, approached the telescope, and popped the achievement.