We recently bought a lawn mower so I saved the box and used it for WALL-E's "body". I cut four 19"X15" squares then spray painted them yellow and silver in the appropriate places. After it dried, I assembled the cube by duct taping it on the inside.
The top was a piece of cardboard with a circle cut out for the head to go through. Again, duct taped together from the inside. I did most of the details before I assembled the cube together.
For the wheels I traced out four WALL-E wheel shapes spray painted them and detailed the front of the wheel with a silver sharpie pen. Two wheel shapes are used for one wheel to give it a 3-D pop out look from WALL-E's body (I used toilet paper rolls to stabilize between).
For the wheel tracks I peeled apart a long piece of cardboard (so the corrugated cardboard would show) and spray painted them black. The arms are cardboard cut outs painted and detailed. I attached sport sweat bands so my son could wear them. The head is an old bike helmet spray painted silver.
WALL-E's eyes were the biggest challenge. Everything was cardboard cut outs and I used the thinnest cardboard I could find to wrap it around while using hot glue. It took a lot of patience to wait for one section to dry while holding it together and doing the next section. I highly recommend hot glue and cable ties for spots. Thin cable ties are helpful in areas where it is difficult to hot glue. Everything can be spray painted to "hide" it.
Lastly, I bought battery operated LED lights found at my craft store in the floral section. These were perfect as they twist on and off. If you choose to create this Wall-E Costume be prepared to help your child walk in it. They will not be able to see their feet (curbs, etc.) and may fall. I was right next to him helping him the whole time.
While working on the Wall-E Costume, I used a small WALL-E die cast figure as my "model". The whole project cost under $20!!