That would be a Master Ball, however, if you don't have it no more, or want to save it, use a duskball or a Ultraball
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After the events of spear pillar check out all of the lakes and battle uxie and azelf, Mesprit will run away Sargent Pickles response: I caught uxie but defeated azelf by accident and i tried like 20 pokeballs on uxie until i had to use my master ball it just would give in lol but u can catch it :)
you can catch the uxie at acuity lakefront rite by snow point city! :D good luck getting a uxie! i caught him wit a dusk ball! oh wait make sure u hav tons of dusk balls! he is in a little cave. from, Pokemon master123
you catch raikou on the last gym leader in the kanto leaders and you catch uxie in vermillion city from
before you do anything SAVE! this is so if you don't manage to catch uxie you can still do it again. firstly get its hp down using a Pokemon with good stats. then get a Pokemon with about the same level as uxie (level 50) and use a low lower attack till the uxie's hp is really low. then use whatever type of poke balls you like (i recommend ultra balls and dusk balls) till u have caught it. hope this helped!
I used a Master Ball to catch Palkia, but that was before I knew Uxie, Azelf, and Mesprit were legendary. It all depends on the types of the Pokemon or how long you expect the battle to last. For Water-type or Bug-type legendaries, use Net Balls. For long-lasting battles, use a Timer Ball. For cave or night battles, use a Dusk Ball. (I recommend this for the Generation IV legendary trio, Uxie, Azelf, and Mesprit.) For Water-types, use a Dive Ball. (I'm not sure where you get this.) An overall ball to use would be the Ultra Ball.