Hey Wynn, I finally got around to looking through my GTS trades and compiling all the Luxury Ball mons I got. All of them are shiny except for the Articuno, Aurorus and the Archipelago Pattern Vivillon. I also have a second Shiny Rayquaza that I didn't list here for some reason. That second shiny Rayquaza, the Dialga, Reshiram, both Zekroms, Tapu Koko and Regidrago all have 6IVs (the Salazzle has perfect IVs in everything but Attack), which probably means they were cheated for, but other than that nothing about them is illegal... assuming you care about that sort of thing. So long as the Pokemon can theoretically be caught like that I don't care too much
As far as what I'd want for them, I still need to look through everything and determine what evolutionary lines I'm missing/don't have easy access to. Anything in Sun/Ultra Sun is within my abilities, save for the version exclusives from Moon/Ultra Moon (some of which I have) and the Sun/Ultra Sun Legendaries since I already caught all of them in both saves. I have Mewtwo, Rayquaza, Dialga, Reshiram (shiny), Landorus, Meloetta, Xerneas, Zygarde, Necrozma, Ogerpon, Terapagos and Pecharunt in Beast Balls that I caught myself, and a bunch of others I got off the GTS, several of which I'm certain were cheated for. The ones that look legit enough that I have are Tapu Koko (JPN), Necrozma, Spectrier (CHS), Koraidon and Miraidon (CHS). The shiny ones that look legit are Groudon, Dialga and Giratina.
So yeah, any Legendaries in Beast Balls not on this list or the above list are ones I'm looking for. More specifically, I'd want Yveltal (Modest or Timid) and shiny Zekrom (Adamant or Jolly) if you're willing to go for that. Other than that, any Gen VIII and Gen IX mons in Beast Balls are also appreciated, especially the ones you can't breed for such as the fossil Pokemon in Gen VIII and the Water Breed form of Tauros
Let me know which of the mons in pic related you want. I'll be here later tonight to trade when you're ready