Sorry, OP was asleep. Didn't quite expect this.

Alright, here we go:

The gif consists of 4 parts:

• The intro, where nothing happens, this is from the original gif.
• The fire-up, also from the original gif.
• The beam, which base-images do not come from the gif, but rather made myself.
• The landing, which is again not from the gif.

I opened frame 9-31 in blender, and added a glow to the eyes, and then the mouth, which was fairly easy, and looks like this.

Then I rendered these out and loaded them into Gimp, on top of the previous 8 layers (the intro).

I opened the last frame and extended the borders of it, added some glow and a beam, which lasts 4 frames. I extended the borders so I could move the layers around a bit for jiggle, and added those on top the 31 layers already there. Intro, fire-up and beam are now done.

I added a few layers of white for the boom.

Then I took one of the earlier frames, zoomed out, and extended the borders again. I stamped out the victim turtle, and placed scorch marks there instead.

I duplicated that file, and gave the laser turtle glowing eyes and shell. saved both, so I have one with and without blue glow.

I cut out the victim turtle shell from another frame, and removed the head and feet, increased the contrast, made it darker and accentuated the cracks in his shell, as if it were burnt.

I composited the thing in Blender, made the victim shell fall down and bounce, and faded the laser-shell over into the non-laser shell. I gave the camera a jiggle and rendered it out.

I added those frames to the final project too, did some fading and it was done.

Just had to do some color-optimization and stuff to get it under 2 MB, but that's it.