Once the back cover is completely removed, you can remove the battery by lifting it from the bottom-left corner.

There is another small gap for help.

You won't need the help of any tool for this.

From now on, be very careful not to damage the tiny metal springs. The next steps will remove any protection for them; they are thin and very easy to break.

If you break one of them, you need to do precision soldering (or just tape it back in place with electrical tape for a quicker but very cheap solution).