Explanation
This might be a bit confusing at first, the reason why this is the easiest way to do this is because the spikes are targetted at your position when the eye flashes about 0.5 seconds after she shoots the second bullet. The only way to make sure that the spikes are the same every time is by standing still while she shoots the second bullet. This is why you need to stand on the edge. That way you don't need quick reactions to the spikes because they will always be the same.
Walkthrough
I won't cover how to do the small spikes at the beginning. Keep running until you reach the middle of the second floor tile from the right then jump straight up on the platform and quickly (but not too fast) get up on the top and hold right. When the spikes come you want to tap jump followed by a full jump.
I hope this helped and good luck killing this RNG fest