How do I catch sawk (the fighting type Pokemon?

The same way you catch any other Pokemon. Granted, they ARE harder to catch than others, but it still has the same concept behind it. Lower their health as much as you can without killing, then, if you have one, use a move to paralyze or put it to sleep. Then, start chucking Poke Balls. Ultra Balls will(of course) work best. It took me a few tries, but they're very useful once you have them. Especially against Lenora. Well, good hunting!

Sawk is best found just outside of Pinwheel Forrest. He is actually common in the dark grass so try there instead of regular grass. Depending on how far you are in the game, either use pokeballs, great balls, or ultra balls. If you are far enough, however, get some dusk balls and wait till night, as they offer the best catch rate out of the four.

Lower it's hp throw a ball and have luck.... I got mine on the outside of pinwheel forest

Go to Sarah Palin's house , trade her your shiny Lugia for her Patrat, then when you go outside a Sawk will challenge you, throw a Pokeball at it, it is a guarantee catch.

If your trying to beat lenora with a fighting type Sawk is outside Pinwheel forest. I would reccomend to train and evole a Timmburr.

If you have a munna get it to use yawn. Pokemon that are asleep are easier to catch.