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So far, the only method that I can think of is using my decidueye with false swipe in order to avoid the take down recoil, the only issue with that is that I would have to constantly be eating leppa berries in order to save on pp. I'm kinda wondering if there is a strat to be had with harvest skill swap trevanant and a different skill swapper/ roleplayer/tracer that is both a ghost type and has false swipe.

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Here's what you can do for the ultimate Beldum chain, provided you have all the Pokemon required:

  • If you want Beldum to have a particular nature (or at least a 52% chance at it), lead with (slot 1) a Pokemon with that nature. It doesn't matter what it is, but if you want to set up Sticky Web, your best opportunity lies in having your fixed-nature Pokemon also be the Sticky Web user, and use that move right away. This will allow you to see whether an incoming Beldum has Clear Body (in which case the ability will pop up and prevent the stat drop) or the hidden ability, Light Metal, which has no particular interaction with Sticky Web and will take the stat drop just fine, if you care about one of those abilities. In exchange for that fore-knowledge about the ability, it will make every single call (whether it's one you want to keep or reject) take longer from the extra messages that appear; you'll have to decide if that trade-off is worth it to you.
  • Immediately switch to (slot 2) Trevenant, Skill Swap for Harvest and Trick for Leppa Berry, as is useful in almost all chains. Apart from possibly the first turn if you decided to set Sticky Web, you will never again present a non-ghost for Beldum to hit with Take Down.
  • Switch to (slot 3) Decidueye and use False Swipe until Beldum is in the red. If it calls in help during this time, feel free to KO the newcomer.
  • Switch to (slot 4) Gourgeist (or Pumpkaboo, either one works). Use Trick-or-Treat to add Ghost to Beldum's types.
  • Switch back to Decidueye. It actually needs to be holding a Lagging Tail, and this step is why: Lagging Tail allows it to underspeed Beldum no matter what, and use Baton Pass to switch in your Mew without Beldum getting to hit Mew (and possibly KO itself with recoil) later in the turn. Baton Pass is an egg move for the Rowlet line; if you don't have that move handy, what you can do instead is let Beldum call for help, and KO the newcomer with Lagging Tail U-turn.
    The slow pivot was necessary to get (slot 5) Mew in safely last turn without giving Beldum an opportunity to hit it. To prevent the opportunity this turn, the first move Mew uses needs to be Reflect Type, taking Beldum's Steel/Psychic/Ghost typing for itself, so that the inevitable Take Down whiffs as usual.
  • Now use the Adrenaline Orb if you haven't already, and everything is in place. You have Mew's Synchronize active, but it doesn't look at Mew's own nature--it looks at whatever nature you had in slot 1 way back at the beginning of the battle. All incoming Beldums will have a 52% chance of having that nature, and a 2% chance of any other random nature. You can have Sticky Web up, if you chose to use that back at the beginning, to let you scout for Beldum's ability. And you have Beldum in the red, unable to hit you and thus unable to take recoil, unless Harvest fails to trigger for ten turns in a row after using the last PP. The odds of going on a long enough drought to get to Struggle after eating any given incarnation of the Leppa Berry are worse than 1 in 1000, but if you want to be secure against even this possibility, you can have one of Mew's moves be Sunny Day. This gives Harvest a 100% chance to trigger as long as the sun's up and the item slot is eligible to be recovered.
  • Mew's other moves should be high-PP moves that are super effective against Beldum, preferably don't have a miss chance, and definitely aren't spread moves (so no Brutal Swing or Bulldoze, since you only want to hit the newcomer slot, not the passive slot). Thief is ideal for this, and then you can choose a move like Knock Off or Flame Charge to round things out. If Beldum calls for help and you dispatch that help right away with a super-effective move, you get a momentum bonus to make the call rate higher, which is why type is relevant here even if your Mew significantly outlevels the Beldum and could OHKO them with weaker moves.
  • Keep going until you see the shiny Beldum called in. Make sure not to hit the original caller at any point; if it fails to call in help, use Adrenaline Orb again (which won't consume the item) just to avoid having to use a move that turn. You can also use your own Leppa Berries or Roto PP Restores from the bag as necessary if Mew is getting low on PP. After 30 successful calls, you reach the maximum tier for shiny rate (about 1 out of 273), hidden ability rate (3 out of 20), and are assured four stats with maximum IVs for everything that answers the call for help afterward. (If you're playing on original Sun/Moon and you let a chain get to 256 successful calls, it wraps around to 0 and you have to face a depressed rate for all these things for 30 more calls before you get back to the usual point. The Ultra games don't have this issue.)
  • So now you've found the shiny Beldum. Success! Now you just have to catch it.
  • Switch back to Trevenant, use Trick to take back your Leppa Berry (if it doesn't have one, wait a few turns for it to be harvested back), then Trick again to give it to the shiny Beldum. Don't forget to Skill Swap so the shiny one has Harvest as well.
  • Switch to (slot 6) original, ghost-form Rotom. Use Thunder Wave to paralyze the shiny Beldum. Now it can never call for help again, which is important because you can't throw a ball on turns where two opposing Pokemon are active. Sleep would give a higher catch rate bonus than paralysis, but you have to keep replenishing it every 2-4 turns; paralysis is something you use once and it sticks around for good.
  • Switch back to Decidueye and False Swipe down to 1 HP. The original Beldum will probably run out of PP at some point (since it no longer has a Leppa Berry to harvest) and Struggle away its last bit of health; just let it, or else put it out of its misery to get down to just the shiny Beldum left.
  • Throw whatever sort of Poke Ball you want to catch the Beldum in, and keep going until you catch it. Unless you're using a Master Ball, you might as well use a Roto Catch Power first if you have one available, as Beldum has the lowest catch rate in the game and you'll want all the luck you can get.
  • Without Roto Catch Power, you'll have about a 1-in-7 chance to catch if you're using a Timer Ball, 1-in-12 with an Ultra Ball, 1-in-20 with a regular Poke Ball, or 1-in-117 with a Beast Ball if you're looking for a particular status symbol to show off with. In original Sun and Moon, Heavy Balls have exactly zero chance to catch Beldum; the formula was edited slightly in Ultra to give you a 1-in-47 chance without Roto Catch, or 1-in-23 with it, but those balls are also in very limited supply in all such games.
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this is incredibly detailed, all i need now is a harvest trevenant, a pumpkaboo and mew. is there a perma event for mew or are those all dried up>. this is a great answer in general, i never would have thought about giving it a leppa berry with trick while having it be harvest. i wish more people (myself included) would put the time and effort into making a good stratagy like this