Here, we'll explain all the things that can help with breeding. Depending on your goal, you may not need all of them. Still, the knowledge would be useful to have.
This hold item prevents Pokémon from evolving, but it has a secret function. If a Pokémon holds an Everstone, it will always pass down its Nature to its offspring. Without an Everstone, the offspring will have a completely random Nature. Therefore, if you want to lock down a specific Nature, you'll want one of these.
You can find an Everstone in a sparkling spot in Turffield, south-east from the stadium. If you've lost it, you can obtain more randomly from the Digging Duo in the Wild Area's Bridge Field or via Poké Jobs. That said, you're at the mercy of the RNG, so please try not to lose your items!
If a Pokémon holding this becomes infatuated, the Pokémon that triggered the effect will also become infatuated. But like many other items, it has a secret function. So long as one of the parents is holding a Destiny Knot, the offspring will inherit a total of 5 IVs from its parents, instead of the usual 3--this is a big difference!
The easiest way to get a Destiny Knot is after beating the game. Once you gain access to the Battle Tower, win a few battles until you acquire 10 BP. Then return to the (first) Hammerlocke Pokémon Centre and buy a Destiny Knot from the BP Shop below the Poké Mart clerks. You can also earn BP from online battles and tournaments, etc.
A Ditto (or Multiple)
One of Ditto's useful properties is that it can breed with any Pokémon that can normally breed. In this scenario, it can substitute for the male or female Pokémon. This can be useful when breeding a particular species that has a larger chance of being male, so you don't need to find a female of that species.
You can catch Ditto as an uncommon overworld encounter in the Lake of Outrage within the Wild Area. In addition, you're guaranteed a Max Raid Battle with Ditto in the Pokémon Den in the south-eastern corner of Stony Wilderness, if there's a rare raid (indicated by a purple beam of light). This is the better option, as it will have some perfect IVs.
If you want to speed up the rate of receiving eggs from the Pokémon Nursery, you'll need to defeat Morimoto in an upstairs hotel room in Circhester (it'll be the first room on the left in the left-hand side hotel). Do so and you'll receive this Key Item. However, you must be the Champion to challenge him.
Trying to hatch a shiny Pokémon? If you obtain all 400 Pokémon in the Galar Pokédex, you can obtain the Shiny Charm from the doctor in an upstairs hotel room in Circhester (it'll be the left-most room in the left-hand side hotel). This Key Item will provide two additional chances for a Pokémon to be shiny.
Pokémon with a Different Language Tag
If you don't have the Shiny Charm, don't worry too much, because it's not actually as important as getting one of these. When you breed a Pokémon with another Pokémon that has a different language tag compared to it, the game will give you five additional chances for a Pokémon to be shiny. This can stack with the Shiny Charm.
The easiest way to obtain Pokémon with a different language tag is probably via Surprise Trade. It shouldn't take too long before you receive a Pokémon from a foreign player. That said, you can't exactly control what you get via Surprise Trade. If possible, try to arrange for a trade for a foreign Ditto, since it can work with any Pokémon.
Pokémon that Speed up Egg Hatching
After receiving your egg, you can speed up the rate of egg hatching if you have a party Pokémon with one of the following Abilities: Flame Body, Magma Armor or Steam Engine. Note that these Abilities do not stack with each other or themselves, so you only need one, not a whole gang of 'em!
Common Pokémon that fit this bill include:
- Litwick, Lampert and Chandelure (Flame Body).
- Rolycoly (Steam Engine).
- Carkol and Coalossal (Steam Engine or Flame Body).
Your best bet is the Rolycoly line, starting from Carkol. Because it's guaranteed to have Steam Engine or Flame Body. Unless you catch one in a raid, in which case it may have its Hidden Ability Flash Fire, which won't work here.
Technically, you don't need this for breeding itself. However, it's indispensable for determining whether your Pokémon are keepers are not, by letting you analyse their IVs. To unlock it, you must become the Champion first. Then battle your way through the Battle Tower until you reach Rank 4.
The process shouldn't take too long and, to make things easier, you're allowed to bring in Legendary Pokémon. You may also want to fight through the Battle Tower anyway, to earn BP for the Destiny Knot. Once you've got it, simply press the + or - Button when viewing Pokémon in your boxes until you reach the Judge display.