Wall jumping isn't really that tough, especially in the place with the green creatures since you're given long, flat walls to work with. Here's a more detailed explanation:
Spin jump at a wall. Once you're touching, you can let go of the d-pad. You can also just let yourself fall for as long as you want, as long as you don't move away from the wall or land.
Press away from the wall, and almost immediately thereafter press the jump button. You should be pressing them nearly simultaneously so that you don't move too far away from the wall before trying to jump off of it.
One thing that used to throw me off all the time at the second step was accidentally hitting up or down on the d-pad as I rolled my thumb from one direction to the other, which would cause Samus to aim diagonally. That stopped her spin, which killed the wall jump. This is why I recommend letting go of the d-pad in the first step. Press one direction, let go, press the other. Since you can fall for as long as you want between the two steps, take your time until you get a feel for the timing.