x) It's probably a good idea to discharge the old battery before you start (if possible).
x) Be patient when disassembling your Flip 4. It takes a bit of time and probing. You don't really need any specials tools; apart from the screw driver, a plastic card (like an old credit card) will do.
x) Be careful with the screwdriver. The drivers have really strong magnets; you can easily rip the membrane, if the tip gets caught.
x) For me, the only way to get the (pretty bloated) battery out was to remove the USB charging port on the other side. This is not rocket science, but makes the fix a bit harder. I disconnected all cables from the small board (2x 2 pin connector, 1x ribbon cable) first. I used a 1/4 drive extension to push -- any thin, longish, and most importantly non-pointy (!) tool will do. Depending on how bloated the battery is, you need to apply quite some pressure. Steady hands. You don't want to wiggle the thing around and break something...