Take a piece of PVC pipe and place it where you want the tunnel to be. Take high pressure water and force it through the pipe. Push the PVC pipe as you are forcing the water through. The water will bore the dirt out, and your tunnel won't collapse because you will have the PVC in it.
I use a pressure washer all the time for putting pipe under sidewalks. Use a tip that gives just enough opening and push the pvc or ads through. Best to pressure down grade so the water and spoils have a place to go. If that isn't the case, dig a hole at the end you will be pushing to and the water and spoils will have a place to go. Your trench leading up to the sidewalk will have to be dug first, so that the pressure washer wand can lay flat and tunnel through with only a slight pitch.