Like you, I have this challenging puzzle game. Although I am not sure how many steps each has, I can say a few things that seems to give both me and other people some trouble in this game. Lol, really obvious mistakes.

First of all, every time a Babel stage is played, it is randomized in a way that is both like and unlike the first. The last time you played a certain stage, you might notice it has been rearranged. So be ready to expect the unexpected. And speaking of expecting- expect what to expect. By that I mean the blocks that come probably have WAY easy solutions that you think. If you are rushing, for example, just calm down and look around.

Another great thing to remember are the techniques in the campaign! I always use the staircase method in most climbs. You know; pulling out blocks farther back after starting from the top until you can't progress any further, then climbing on.

Anyways, definitely look at the single-player techniques!