If anyone has ideas how to keep the robot's other hand on the barrel when the barrel follows the pipper, I'm open to suggestions!
My suggestion: Don't make the other arm part of the bones animation. Instead, fix the hand to an image point on the gun, have the forearm set it's angle to match the front forearm, attach the upper arm to an image point on the elbow, and point the upper arm towards an image point on the shoulder.
Since they're always behind the player, and covered by the gun and the body for the most part, you won't be able to really see if the parts don't line up perfectly.
Bonus points: Draw the fingers holding the gun barrel directly on the gun sprite itself.
Also, I'm wondering why the robot needs to lift his gun up anyway...? That might be handy if it didn't have mouse aim (and could only shoot left/right) and needed to lift the gun to shoot over obstacles while crouching or something, but since there is mouse aim it's not all that necessary and just looks a little awkward.