I've been considering making one of those...
anyway, when I animate the shot, I first have the minifigure point the gun at his target, then I move the gun up a respectable amount without easing in, in that frame, I also like to shine a light onto the guy to make the set look as if the flare which I'll add later is casting a glow on the set. For the next frame, I move the gun up further, with the light shining on the set, but have it be way further away to cast less light, then two or three frames of the movement easing out without the light.
It also helps to move the body back with the arm just a slight bit, and add a little bit of twisting of the minifigure to make the movement a little more realistic.
The lights also are useful for telling which frames you wished to edit in post production.