It surely is possible, but it would be very expensive ! A combination of a lycra undersuit, such as Vox suggested, with urethane rubber raised parts would yield an awesome result I reckon, and might be more flexible and durable than using worbla, but a whole lot more expensive than foam.
You'd have to sculpt or 3D design and print all the pieces, then mold them and cast them. Same for the cowl, a thin urethane cowl would blend in the suit just right.
Unless you know yourself how to either sculpt in clay or model in 3D the design and have free access to a 3D printer, and how to mold and cast things, I don't see how you'd be able to keep it under the 1K$ mark. And if you have to use shapeways or another commercial 3D print service, you can easily triple that amount probably ! You could try to make a run to recuperate some of the costs, but it looks to me like every parts must fit together rather precisely, which means it would need to be custom designed for your body, and thus would not fit most other people unless they are close to your exact measurements.
All in all, depending on your budget, I'd start with the lycra dye-sub anyway, then either look into a foam build, or a urethane build