when he is insanely low - less than 1/4 cm of hp
At any time--the catching of Azelf comes mostly down to luck. For example, I currently have Azelf down to one HP and asleep; however, I have used fifty five dusk balls and still he continues to break free. This is because Azelf has a 3% Catch Rate out of a hundred, which is low enough to send people to mental institutions. It is highly unlikely lowering its HP amounts to making up for the remaining 97%. For all intents and purposes, catching Azelf is more up to chance than timing or HP lowering. That's not to say don't do it; just take the advice with a grain of salt.
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I would use a dusk ball.
Unless you have a Master Ball to spare, Dusk Balls would work best. Timer Balls will work just as well as Dusk Balls if the fight has gone for more than 30 turns.
a dusk ball when he is on yellow but use a 23 and under Pokemon and you can find the dusk ball at the inside of the Pokemon legue at the right counter
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.
u should us eempoleon or garados and then use a dusk ball