Use a heavier plastic opening tool or spudger inside the gap that you began to open up, sliding it further down each side of the case.

You may find it easier to go in short steps, prying the rear case away from the frame slightly before advancing

There are 3 plastic clips on one side and 2 on the other; in these areas you will have more resistance when sliding/prying. Slowly apply more pressure and they should release with a click