Separate the lower half from the upper half.

The upper half of the calculator contains almost all of the components except for the piezo "beeper" element, and there are no interconnecting wires between halves.
plastic hook

The only obstacle is the snap-together "hooks" that David Holmes refers to. These hooks are positioned near the [A], [F], [SIN], [1/x], [ON], [+] and [.] keys (the one by the [.] key is a real bugger!). Refer to the cutaway diagram below for details.





Key overlay here ___
                    \     ____________
                     \   |            |
             ____________|    ______  |
                             |   _  | |  <--- Upper section.
                             |  | | | |
             ________________|  | | |_|
                             |  | |___  
  Circuit board and other    |  |     |
  components (affixed to     | /      |  <--- Lower section.
  upper section)             |/__     |        Has a lip which 
                             |   |    |        engages with metal 
           Metal "hook" ---> | / |    |        "hook" from upper 
                             |/  |    |        section.
                             |   |    |
             ________________|   |    |
                                 |    |
To separate the two sections, you will need to push the lower section out and down around the hooks. You can't do this from the outside because the upper section hangs over the lower, so you have to go from the inside. Luckily, the six slots in the keyboard (used by the separate user-overlays that fit over the original overlay) near the [MTH], [ENTER], [blushift], [NXT], [backspace] and [-], come in handy for this. These slots are not exactly lined up with the hooks, but are close enough. You can insert something in these holes (I used a jewelers screwdriver, flat head) at an angle that is mostly down and somewhat out, to a depth of about 5mm, and come in contact with the lower section. Push the lower section out about 2mm (this will take a bit of force), while wedging something in the outside gap to separate and hold the sections apart while working on the other hook positions ( a wooden matchstick works). I recommend starting with the [A] or [F] positions first, working down whichever side you started with, then do the other side, and leave the [.] position for later (there is no helpful slot there).

 opening  closeup

 

Remove the battery cover and the batteries.

 The two battery contacts which come through the case will need to go back through the case when the sections separate. The upper contact is hooked on a plastic boss, and needs to be freed from it. Just pop it off with your finger or a screwdriver.
 plastic boss closeup

Very carefully pull the two sections apart at the top

(above the screen).
If you have freed all the hooks, the case should sort of hinge at the bottom edge. This is due to the last hook (near the [.] key). Some careful twisting and working of the sections should free this hook as well. You should now be able to completely separate the two sections. I recommend at this point that you take a pair of pliers and flatten that last hook so that it will not hold next time. It is really not needed anyway, as the other six hooks hold the unit together just fine.