This is an extremely long level that covers the majority of your time in the Vatican. Due to its length, I have broken down the solution with videos so if you are stuck on any part. You should be able to find the right video to help. Not all parts are necessary (such as mad priest and Savage discovery) but you will probably need to do one of them to get the money for the camera
The Stolen Cat Mummy starts very early in the game after the mission 'The Break' In which is part 3 of my playthrough.
You will start at Castel Sant'angelo and the main task here is to enter the Vatican. It will also act as a combat/stealth tutorial.
The next video is for the mad priest. This is a side mission but is useful to get coin for the camera you need to buy and also has its own achievement, you can start it by reading Catherines Letter, found on the table on the left from the room where the Camera is sold
Next I did A Savage Discovery, which again has its own achievement.You can pick up this mission in the tent after you leave the first building in the Vatican.
I started it after the mad priest as the professor you speak to first is located close by.
Now back to the main mission for the Stolen Cat Mummy as you will now have enough for the camera. This video will show you the locations of the 4 photos you need to take before returning to Antonio and heading to the tower. It covers the puzzle with Jesus 5 sacred wounds towards the end of the video
The next part takes you through the rest of the crypt and how to escape and sees your first meet with Gina
A Nun in Trouble will start automatically and sees you teaming up with your new accomplice in the search of her sister. It covers the what to photograph in the storeroom which you need in order to proceed
Up next you are tasked with solving a fountain puzzle so this video includes the solution and also the Trials of Augur
Once the trials are done, we are into the final stretch of this mission which will see fight a giant and stowaway on an airship. This will net you the achievement