The hardest part for me was finding the right size bottle that could be easily cut on both ends. After a few failed attempts, I found that Old Grand-Dad worked a treat! I used a roller-type bottle scorer, then shocked it with a candle and an ice cube.
Instead of using an Arduino and a shift register, I used self-flashing LEDs. Since each LED's flash rate is slightly different, the UFO looks like it is randomly making different light patterns. Soldering the 100 ohm resistors to each of the LEDs isn't so bad if you have some music going.
I used Meshmixer's "Plane cut" tool to cut the cow in half and print it in two parts. After assembling the halves with SCIGRIP 16, I epoxied a stiff wire to its leg and primed the cow with Gesso. Then I used cheap acrylic paint on the cow.
On the lower half of the UFO, I drilled out some spots for a micro USB female breakout board and a small slide switch. I used hot glue to anchor these in place. It's now easy to power the light from a USB power bank.