OK, you are going to have a trench under the walk....keep it as narrow as you can. When you are done try and block off one end with a plank..on the low side. After the plank, backfill the trench to give it support. Then from the open end start filling and tamping with whatever fits. Ram it right against that board you put in. Pack it in...repeat until you get to the top. Then pull the board and backfill.