You first need to complete 3 chapters in the story mode with a gold award to unlock this level.
I think the easiest and best way to do this is with 2 controllers.
I put a pillow on my lap so the controllers didn't slide around and kept at it til I got it.
As you can see in the video, I barely made it.
Sometimes I would switch from this to Obelisk in case I was getting too frustrated, but patience and persistence are the keys to getting these.
I try to make each platform as flat as possible with a broad base even if it seems like I'm wasting too much time. This is more important on the later stages of Babel.
Watch what happens when you pull out or push a block out and what the consequences are. For example, when you pull out a block out from the end of a row, if the row above has an unsupported block that sticks out 1 block farther, that block always falls. That's why in the video I posted, I always try not to pull out a block on the end of a row if I can help it. Unless that will help me where it will fall.
Here is a page from the Catherine Wiki site with a lot of great advice on Babel:http://catherinethegame.wikia.com/wiki/Babel_Tips
Even though it says elsewhere that the blocks are random, they aren't. There are only a finite number of combinations and there are only a relatively few different patterns that come up. You'll notice that the patterns are very similar from game to game. Not exactly the same, but similar.
I got this from the Catherine Wiki page posted below and above.
This page below also has some good info on Babel in general too including approximately how many steps for each babel level in both single and paired modes and a few videos on the single player:http://catherinethegame.wikia.com/wiki/Babel
There are things to remember in paired mode. Both must survive and don't block your partners path. I know it seems obvious, but it's really easy to do.
The key to this is patience and practice, if I can do it, so can you, good luck.