what's your strategy for catching legendaries?

Let's see if I can remember my old setups...

1. throw Quickball (because why not)
2. if it's a Ghost Type/immune to Paralysis (often times I prefer para over sleep, because it's permanent) -> use Soak
3. put it to sleep/paralyze it
4. get its HP down to 1 (False Swipe is the best distributed of those moves afaik)
5. use balls that fit the situation best (some are better than Ultra Balls in certain situations)
6. at some point start using Timer Balls
7. either success or restart of the capturing process

In case an ability prevents the Legendary from being statused, then picking something like Mummy or one of the ability changing moves is a good way to still get a status on them.

If it tends to explode for whatever reason you may want Sleep+Damp.

Healing items are obviously nice to have, especially if you have to deal with weather or status conditions.

Most people would use Smeargle as part of their capturing strategy because it does role compression best. However, I tend to pick whatever and try to come up with a strategy that makes it work.

In terms of Nature a fainted Synchronize mon with respective Nature at the top of the party does the trick well.

It really depends on the kind of Pokemon that I have on my team at the moment, but I generally go for accuracy reducing moves first so I have more of an opening to reduce their health, and then if possible, inflict status conditions like paralysis and sleep.

The accuracy reducing moves are pretty important because you don't want the legendary in particular trying to whittle down your Pokemon's health while your tossing out Pokeballs trying to catch it.