First off, IVs (or Individual Values) are stats that the Pokémon are “born” with. They cannot be changed, with the exception of Hyper Training. A Pokémon has anywhere from 0-31 IVs per stat.
This means a Togekiss with 0 special attack IVs will deal significantly less damage than a Togekiss with a perfect 31 special attack IVs.
This mainly matters for competitive battling and relies heavily on catching raid Pokémon and breeding. If you’re just trying to beat the game with your rag-tag group of ‘mons, you don’t need to focus on IVs at all.
Catching Pokémon with good IVs
Unless you get lucky, most wild Pokémon you catch won’t have outstanding IVs. While getting a Pokémon with maybe one or two 31 IVs isn’t completely unheard of, you’ll want to grab high IV Pokémon through Max Raids.
The raid Pokémon can have anywhere from one to four perfect IVs, depending on the difficulty of the Max Raid battle. The harder it is, the more perfect IVs it will have.
Even better, you can grab a Ditto from a harder raid to get a three or four IV one. From there, you can just breed whatever perfect IV Pokémon you want.
Breeding Pokémon with good IVs
Once you grab your good IV Pokémon from a raid or get a Ditto with good IVs, the goal is to make a Pokémon with at least five perfect IVs.
To get a parent Pokémon to pass down IVs, give it a Destiny Knot to hold. This passes down five of their IVs to their child, randomly. Having a parent hold a power item that’s used for EV training will have the parent pass down the corresponding stat guaranteed. The Power Weight will pass down the HP IVs of the holder, the Power Bracer will pass down the attack IVs, and so forth. All of these items can be purchased from a NPC in the central Hammerlocke Pokémon Center for 10 Battle Points each.
If your Pokémon focuses on physical attacks, they won’t need a perfect special attack IV and vice-versa, though there’s nothing wrong with getting a fully perfect Pokémon for the clout.
Hyper Training using Bottle Caps
Once your Pokémon is level 100 and you beat Leon in the Pokémon League, you’ll get the option to Hyper Train it at the Battle Tower. In exchange for one Bottle Cap, the trainer will max out one of your Pokémon’s IV stats. This means if you pick HP, they’ll max out its HP IV to 31.
Note that Bottle Caps are extremely hard to come by, and you should use them wisely, like on Shiny Pokémon.
Gold Bottle Caps, which max out all the IVs for every stat for the Pokémon of choice, are even more rare and only obtainable through competing in the Battle Tower and digging them up using the Digging Brothers.
Hyper Trained stats will not pass down through breeding, so making a Ditto with Hyper Trained perfect IVs will not work.