Don't bother trying to run up the stairs. Just hit the first button at the same time as you jump to where the stairs should be, and you have to hit the second button when you're leaving the second block. When you land on that 4th block, jump to the platform...don't try to walk to it.
This wall jump is pretty easy, just start from the far right of the platform before the wall, and sprint jump around & aim at the closest corner. Shift as soon as you land.