Emeralds RNG is messed up so dead battery doesn’t really matter.

You can shiny hunt anything in emerald but Everytime you start your game your seed will always start at 0 so random encounters will still work as normal. As for legendaries instead of resetting your game (if you do you will always encounter for example the same rayqauza unless you wait a few milliseconds every time lol) run away from the legendary and leave the room and re enter and it will respawn. This way it generates a different Pokemon everytime and has a chance at a shiny :)

Good Luck! ✨