Yep, the big plastic cover has to come off. The sheetmetal box houses the evaporator coil and blower, where the actual cold air is made. The compressor itself has two metal lines coming off of it, the larger diameter tube is the low pressure side and that's what you want to insulate. If you felt these areas while the unit was running you'd find them quite cold, and the more cold kept inside the better.
I traced the outline of the box onto the Reflectix material (it comes in a roll) and cut the panels out with scissors. A little spray adhesive bonds them in place. There's a service panel on one side that you don't want to use glue on, so I used some strips of self-adhesive velcro to make the Reflectix removable.
You'll have to punch a few holes in the Reflectix for the cover's mounting screws, but that's about it.
Here's the materials:
Shop Reflectix 33.3-sq ft Reflective Roll Insulation (16-in W x 25-ft L) at Lowes.com
Shop Frost King 1/8-in Rubber Plumbing Pipe Wrap Insulation at Lowes.com
Do a search and you'll find a lot of other similar ideas, see what works for you. I have no idea how this will affect your warranty so proceed at your own risk!