Cute bag. I just watched the video by the designer that is part of that link. I guess it's worked from the inside out starting with the circle whorl patterned square, when that's finished you pick up stitches around the outside and work the next section, etc. So, I think you'll only be using 2 colors at any given time so that should make it a little easier.
I would suggest reading the entire pattern first, then work slowly and methodically. Don't be nervous. It's just yarn. Here's my mantra when trying new things: "What's the worst that could happen? You frog it and try again."
Let us know how you make out.