Depends on your luck.
I mean, lots of people have to reset a lot, while I got lucky and caught it with my first ultra ball just after my Charizard burned him.
I'd say, forty Ultra Balls.
first buy as many ultra balls you can and battle Mewtwo. Once his hp is low start using the ultra balls (just keep trying until you got him)
About 30 I would say
about 20
well for me it took me 20+ ultra balls. It all depends on how lucky you get.
You need 21 ultra balls to catch Heatran
Since Mewtwo is in a cave, try using Dusk balls. If it doesn't work, Master ball. If you already used the Master ball, then buy as many Dusk balls as you can and try to catch it. If your patient enough, try catching Mewtwo with full health.
If you are good at catching legendaries, then you would need at least 10 but 15 would be safe. If you are not good at catching legendaries, then I would get 25 ultra balls.
for me what i did i didnt have any ultra balls all i had was 10 great balls and i used mega kick with my blastiose and used about 5 great balls and caught it :^) -drew
i caught it first time in a great ball
depends on how weak he is and how lucky you are
There are many types of PokeBalls you could use to catch Azelf.But I would suggest the following: Quick Balls Master Balls Poke Balls Dusk Balls and,Ultra Balls
it takes at least thirty i caught mine with a ultra ball but before i did that i lowered its health to almost red at the end of yellow use a few dusk balls and great balls before using ultra balls