The first boss is a ball of blue light residing in an idol in the middle of the area.
To kill it requires multiple steps, but follows the same pattern.
First, it will fire bullets one at a time at you. Climb on top of the idol and use you pickaxe to hit it from above until the pillar breaks.
Second, it will begin to rapid fire burst three at a time while flying. Jump from the small exposed rock onto the idol and hit it until it goes berserk.
Finally, it will begin to shoot waves of bullets in all directions. Run-jump from the long platform onto the idol and finish it off.
In all forms, the idol will shoot three times before overloading and powering down, for a few seconds, long enough for you to hit it a few times.