It's been a while since I caught a legendary without a Master Ball. I was pleasantly surprised that I caught Mesprit in 11 turns and used a Dusk Ball. I want to catch a shiny Zekrom/Cresselia at some point without using my Master Ball.
I'm going to 4-Up you here. Easy catching guide for the Uxie/Mesprit/Azelf trio: use Dark types due to Psychic immunity. All moves available to them are, by who uses them, Future Sight/Extrasensory (all three), Yawn/Amnesia (Uxie), Lucky Chant/Charm (Mesprit), and Uproar/Nasty Plot (Azelf). My premium choice was a Crawdaunt with False Swipe; it was immune to Future Sight and Extrasensory, and most of what was left (Yawn, Amnesia, Lucky Chant, Charm, and Nasty Plot) had no impact after I got the subject down to 1 HP, leaving only Azelf's Uproar to worry about.
Uxie, at 8 PM, was my first attempt yesterday. It went into a Poké Ball without much trouble.
Azelf was a pain and took several attempts to get down to 1 HP. Once I got it there, I lost all my Pokémon and dropped over 5K, so reset and retried. This time, my Lv.46 Crawdaunt stood up to Azelf's Uproar long enough to get its HP down to 1, and I had a few knockouts. This caused the Nameless Cavern to disappear from the map as the KOs temporarily reduced friendship.
This morning, I wandered the waters around Mossdeep to regain friendship with a few levels and chanced upon a Shiny Pelipper, and thankfully I had Crawdaunt handy for the catch. Following this battle, I got the Nameless Cavern back on the map, and Mesprit was another easy battle. However, I used 47 Poké Balls, then had to reset because I ran out; I did test and catch on the fifth Great Ball, but with such an easy battle I was using the regular ones as my money is short after buying some Revives (I need to do some rematches or clone my expensive Comet Shards). The second attempt went on the 22nd toss.
So, to sum up, all three in the trio in regular Poké Balls, and a Shiny Pelipper as a bonus. That's a pretty good 24 hours! As for why I used regular Poké Balls: I did the
entire Safari Dex from X/Y by catching
every Pokémon with
every ability in the Friend Safari (did I mention they're all female except for male-only and genderless species?), so I'm continuing the old-school methods with everything except the storyline Groudon, which I sealed on the 10th Ultra Ball very early Christmas morning (Rest is too much to deal with at the level you likely encounter it at). I made an exception for a Poochyena with a good Egg Move when I ran out of Poké Balls in one game.