This achievement pops after you finish the final level where you climb the alien tower.

See I Am Arthur Clark achievement description for more info. 

Only 1 in 148,000 is expected to obtain this achievement and so far nobody has. I doubt 148,000 people even bought this game for that matter. If you were hoping for an experience like Limbos less than five deaths achievement then you will be very disappointed. This game is far longer and harder and isn't half as good. I honestly doubt anyone will ever get this achievement.

This achievement doesn't require a perfect run but does require a near perfect run. Keep running and jumping occasionally as it makes you travel faster. Try to time your jumps at the last second so that you don't end up hanging off the edge of one of the buildings and losing time. The achievement should pop when Arthur starts talking after you jump off a series of buildings being lifted by the Tripod. If you mess up along the way you can always restart the level.

You can obtain this achievement when you reach a giant bell tower you must climb. After you reach the crate at the top and begin your ascension keep an eye on the left hand side of the tower. Above the second drone down from the top you will see a random crate on a ledge. Simply push it down onto the drone and the achievement is yours. This is the first achievement I got in the game and just popped randomly during Barthurst Mews. It may pop randomly for you as well. You can also achieve this legitimately in Hyde park level by following this achievement video.

This should be the first achievement you obtain in the game but can be missed. When you get to Barthurst Mews you will be in a mob of people running back and forth. The Tripod will begin snatching random civilians one by one. Simply jump onto the claw of the first civilian the tripod latches onto and the achievement will pop when it drops you off at the top of the building. If you miss it you can just restart the level.

This is going to be the hardest obtainable achievement in the game. There appears to be no distinct pattern to the drones and they often detect you through solid objects. Use the restart level option if you get spotted or die in any place. This will take a lot of patience, trial and error.

When you are traversing the apartment buildings with the black gas you will obtain a gasmask. Along the way you will run into a little girl that runs away from you. Be sure to approach her slowly and Arthur will give her the mask. Story related, can't be missed. See the YouTube video if you're having troubles giving Jenny the gasmask.

After completing a puzzle under three trapped soldiers you will take an elevator up and find buttons to open the doors trapping all three. Two of them will take the elevator and exit to the left while the third will take the elevator to the top to assist you with unlocking doors as you progress. Eventually you will reach another cell containing many guards. You will need to free them in order to progress. The achievement pops after the door opens. Story related, can't be missed. 

Complete the level Hyde Park. Story related, can't be missed.

Complete the level London EC4 Underground. Story related, can't be missed.

Complete the level Stamford Street, South Bank. Story related, can't be missed.