Shiny hunting for Metagross in Emerald specifically is possibly one of the hardest hunts in the entire Pokémon franchise. This is because Emerald has what’s called a fixed seed, which this video explains pretty well. In a nutshell, it’s a glitch with the RNG that makes SRing for shinies impossible on almost every save file in Emerald. If you have Ruby or Sapphire (with a working battery; a dry battery also results in a fixed seed), I highly recommend hunting for it there instead. However, if you’re dead-set on getting a shiny Beldum in Emerald, there are a few methods you could use.
The most straightforward hunting method is to get the Beldum from Steven’s house and then breed for a shiny. Although Beldum has a slow hatch rate, and there’s no Masuda Method, so you’re going to be up against the full 1/8192 odds while only hatching 1 Beldum every 2 or 3 minutes. If you decide to do this, then as long as you’re not resetting after every egg, you shouldn’t have to worry about Emerald’s glitched RNG at all.
The method that I would personally use is the Battle Video method, which is basically SRing with extra steps. This video explains the method.
The quickest method, however, is to use RNG abuse, although that’s pretty complicated, requires that you know your SID (secret ID), and needs very precise timing. Basically, by plugging your trainer ID and SID into a program like RNG Reporter, you can find a specific frame that would yield a shiny and aim to receive the Pokémon on that frame. If you want to try this, then this answer provides a pretty comprehensive guide to how to find your SID (since it is a hidden value) and get started, but you can also use Smogon’s guide or Google other articles to help you out, if you’re having trouble figuring it out.
However, some people would argue that RNG abuse is illegitimate, so keep that in mind if you’re against hacking and the like.