Will I definitely lose my save state while replacing the battery?

Open the cartridge and plug it in a GBA. Turn it on and exchange the battery while the system is on. Just make sure to not touch any contacts that could damage the cart, focus on the battery and make sure it doesn't lose power while you're working on it.

This works because when the batteries start to wear out, they can still work through the GB's own battery, but once that one also runs out, you'll be out of power for both the cart and the system.

There are ways you can copy the backup data from the cartridge to your computer.

It'll cost some money in buying the hardware to do that, but IMO it is way safer than replacing a battery while the device is on.

The accepted answer is flat out wrong, problems with it include:

• It will be very difficult, if not impossible, to access the cartridge while it is inserted into a Gameboy. It will be easier with a Gameboy advance as it will stick out some.
• Gameboy cartridges are very difficult to open; they use a proprietary screw that is exclusively used by Nintendo. A specialty tool can be obtained from specialty suppliers, but they are necessarily pricy.
• The battery back-ups in Gameboy carts are soldered in, you cant replace one without a soldering iron.

So even if you bought the tool, disassembled the cartridge and inserted it into your Gameboy, your not going to be able to de-solder the battery and solder in a new one!

If you want to replace the battery you will need to power the volitile memory with an external power source while you change the battery.

Years ago I tried replacing the battery in a Gameboy cart. I did a lot of research to find the correct replacement battery and read the tutorials. I had to cut it open because i didn't have the proper tool. After I replaced the battery the save file still didn't work. In my case it may not have been the battery.

I suggest you try this with an expendable cart first, or find/buy a way to get the save off the cart first.