Edit: I tested whether Skill Swapping Synchronize onto your Pokémon would affect the natures of new wild Pokémon, and, after over 10 tests, have concluded that it does not work. I have reworked the Beldum-chaining method, but this one is much less stable. I would recommend Masuda Method to anyone that wants a comp Beldum.
I chained for a comp shiny Beldum a little while ago (Edit: and was extremely lucky because I somehow got a Jolly one on the second try), and you'd be surprised how easy it is to chain for once you get it set up. Here's how you can get one:
- A Phantump/Trevenant with Harvest, Skill Swap, Trick, and a Sitrus/Confusion Berry (I would use a Sitrus Berry, since it doesn't need to be at 25% health to activate).
- A defensively bulky Pokémon with the ability Synchronize, the nature you want your Beldum to be, and that knows Sunny Day, Protect, and an attacking move (Umbreon is your best option).
- At least one Adrenaline Orb (although preferably more), and lots of Leppa Berries
- (preferably) A Pokémon with Thunder Wave
Once you get all that, encounter Beldum and do the following:
- Encounter Beldum with Phantump/Trevenant and use Trick and Skill Swap.
- Send in your Synchronizer and use Sunny Day whenever the sun is not out. Take out any non-shiny Beldums that appear, and Protect if you ever get into a situation where Beldum might take itself out (which should be just about every other turn if you're using a Sitrus Berry).
- Use an Adrenaline Orb to increase the call rate. If any of your Synchronizer's moves run out of PP, use a Leppa Berry.
- When you find a shiny, you can either switch back into Trevenant and Trickswap the berry/Harvest from the old Beldum to the new one, or you can go directly into your T-Waver
- Switch into your Thunder Waver and paralyze it so it doesn't call for help (if your T-Waver isn't a ghost type, then the old Beldum will conveniently take itself out here. Otherwise, take it out after paralyzing the shiny)
- Happy catching!
Sunny Day will make it so that Harvest unfailingly recovers Beldum's berry every turn, negating the recoil from Take Down/Struggle. On turns when a new Beldum doesn't appear, you can use an Adrenaline Orb to waste a turn. If you use one when one's already been used, it'll use up the turn, but it won't waste the item. If you don't have spare Adrenaline Orbs, you can also attack the spot next to you; SOS battles are set up like Double Battles where you have no partner, so attacking the spot were your partner should be will just cause the move to fail and waste a turn. This is not as good as the Adrenaline Orb trick, though, since that uses up PP.