That slope above the wall is a moot point. That wall is already 6' from the looks of it, add the top of that hill in the picture and your looking at probably 12' to the bottom of that wall. That means you need to open up the top atleast 12' or more away from the wall depending on how your ground is. If its good ground you wont have to open it as wide, but it still needs layed back for safety. From the looks of it you might have to take out a few trees or bushes for this? It would be a serious cut. If you used a 5 ton hoe like Alex said, you could do it in a couple of cuts. Some operators might try it with one.
If access is an issue get two smaller excavators that fit through a 36" gate. Bench one machine down and pass the dirt off to the the other one above him to get the dirt out of the way.
The golden question in this job is if you can get a machine up there, and work a safe enough distance away from the wall to make that first cut. It will have to dig its way along the top of the wall to notch out the hill top to get up there.