By putting a thin spudger between the two halves of the plastic container, it is fairly easy to separate the two halves. But the top likely won't come apart without a fight. There are two primary pieces to keep in mind:

The small clips that show "L and "R" should probably be removed before the two pieces are separated. They are clipped into the outer shell and adhered with a similar adhesive to the outer rings that were previously removed. The trick: spread one side outwards as you are prying the broad section away from the rest of the shell.

Now to the main issue: there are deep "tracks" that clip the two halves together. I haven't been able to use a technique to make this easier, as you cannot "slide" the two halves apart. Just like the L/R clips, concentrate on stretching the inner (grey) part as much as possible. Force will be necessary; leave a comment if a better way is found.