Coma State Eden has had an update to the game's controls.

On gamepads, you can now shoot with the face buttons, the directions correspond to the directions on the right stick.
So if you want to shoot the boomerang, top face button. Left/Right face buttons for the standard laser.
Bottom face button for the drop-shot.

In addition: this also means that if you want to use a gamepad that doesn't have two control sticks, it's now possible.