I did research years ago on how to do this. The way I'm following, I turn over ALL the grass and create a new stable foundation for the stones. BUT this bed will be different in that it has to be RAISED off the ground to be flush with the path. This is different than just doing it on level ground. The ground is NOT level so... This is the border.
Leveling the 1st corner. Notice that the bubble IS in the middle! lol! Seriously, I have to raise the ground a bit to be flush with the path. My parents will at a later dirt bring in new dirt and make the whole area level with the path. And yes, a rototiller WOULD help to an extent.
Tools of the trade. What does Thomas's wheelbarrow have to do with it? He was helping us move gravel earlier. You can see the location of the 1st corner WITH bricks. I am using the old grass to raise everything up.