You have to "glitch" your way out. There is a lone box on the right side of the screen with a lightbulb in it as the level starts. Get the first 2 lightbulbs, then head for that 3rd lightbulb. After you've shifted into the box to get the lightbulb, start jumping around in the box (I prefer aiming for the top right corner). Make sure you're jumping fully and hitting the top of the box. Eventually, hopefully, you'll get "glitched" to the top of the screen, ideally right on top of the arrow (sometimes it puts you in the spikes to the left and you die; sometimes you just disappear into thin air). Keep jumping around in the box until it works. After you've been "glitched" up you may have to trying walking right or jumping again if you don't land on the arrow, or you may have to restart the level and try again. It worked on both the iPad and iPhone. It should work eventually. It took almost 4 months to find the solution online, but, like the Shiny Ponyta, I finally found it...
I jumped found in the box like Arrupe described and got right through! Thanks for the tip Arrupe. Now I need some help with level 109. I cannot seem to control my shifter finely enough to avoid the spikes. Any tips for that level?
I jumped around in the box for a while and it worked second time. First time I ended up on the spikes. Arrupe suggested aiming for the top right corner. This didn't work for me. Jumping around did the trick.