Thank you for the images, but those will likely be deleted as well, as per
the guidelines (see point #9), so I've prepared a new bunch with thumbnails and some directions that will hopefully stay here for as long as the forum is.
Here is how you insert a fine nail file or any similar object that will let you pry the plastic corner just a little bit so you can put the file in parallel to the border and then gently push it in:
As the file goes in like 2 cm., a plastic hook will give in from its position, where it holds the corner cap in place by resting against an inner wall of the cap. The cap is already removed here so you can see the hook:
When the cap is unhooked it can be slid a few millimetres along the reader border, and then removed by pulling to the side:
Both the latch and inner wall can be seen to both sides of the file here for your convenience so you can imagine how they come together when in place:
Repeat the process with the three remaining corners.
Now you want to make sure you removed the stylus and torx screws and start prying the case open from the edge where the ports are with the file, just a little bit, from its centre. After the grey case halves come apart a bit at the corners, it's time to pry from the sides. Each corner has several openings on the back side of the white plastic frame where you can insert a flat head screwdriver and very gently pry so the back case half starts coming apart from the corner up:
The plastic stubs between every two openings that hold the back case into place will likely get damaged as can be seen in image #5, or even broken off (they are very fragile). Don't worry, the case will still fit snugly anyway, and then there are the corner caps.
After you are done with opening the first lower corner, do the other lower one, then do the two upper ones gently, from the reader side centres to the corners, and when you are done do NOT pull the back case out, remove it like it is hinged to the front case on the upper side, so the latch that holds both together near the stylus holder won't break.
You can replace your battery now.