I was inspired by the NCLA Nail Wraps: Flash Fete. I really love this design, and it's not as hard as it looks.
Start with a white base and drybrush some blue, purple, yellow, pink color over it. You can add some black too, but be careful with it! When you satisfied with the colors add some black lines. Step 8: use an iridescent nail polish to create that shiny/duochrome effect.