OK, here's what looks like they did. They did the standing animation, then simply took that same stance and set it off by like -1, 0, 1 in the x-axis, -1, 0, 1 in the y-axis (not necessarily in that order) in another animation file of the character, with the time between each frame being about 2 ticks. They set the "shaking" animation to have the a1 option on (transparency) and layered that behind the single standing animation. You could code this to be done in-game if you wanted quite easily.
The in-game coding would best be effected by using the shaking animation as being an "Explod" that is bound to p1. The explod itself is simply an animation that appears (I say this for newbies), so by setting the explod to be the shaking, "alpha-fied" animation, you easily achieve the desired effect here.