The way the system works is that there is a ball joint that acts as the main pivot for the headlight, it's what you see in the upper left corner of the headlight picture, and the upper right corner of the mounting bracket.
Then there are two adjusters that rotate the headlight up/down and left/right about the main pivot (you see these in the upper left and lower right corners of the bracket in your photos).
There is also a spring that takes out slop.
As others said, you want to unhook the spring. Then, I always back off the adjusters all the way out. The hardest part (probably what you're struggling with) is disengaging the ball joint, which is a snap fit. It takes a tremendous amount of force to unseat it, to the point where you think you're going to break the headlight. But that's what it takes.
Study the photo carefully to know where the ball joint is, then pull on that sucker.