In your shed build a room with well insulated walls with the freezer compressor built in. I know a guy who built a cooler like this for his bar. Just make sure you insulate and build the walls opposite of the way you would a house wall, think of the freezer as the exterior space. Let the inside (cold side) of the wall breath and the outside (warm side) wrap in plastic. Possible combination would be:
Freezer Space
1/2" plywood
Tyvek
1" styrofoam insulation
2X6 studs with 5 1/2" bat insulation
1" styrofoam insulation
plastic wrap
1/2" plywood
Exterior Space

If you build it with the warm side able to breath, I believe you'll end up with moisture problems, you may either way, but the cooler space should be dryer air so it shouldn't be as great of a problem.

Good Luck, it's just an idea.

Paul