ooh, I really should have people know that you can use the walls to your advantage.
the thing with the walls is that if you bump them while having a Y velocity moving upwards, it adds an additional force to push you higher
Oh yes I got that right from the start. I don't think an explanation is necessary. I managed to do the first 4-5 jumps, got stuck where there's a vertical wall you bump your head into on the left.