So if you are like me and really want to catch Necrozma in a beast ball (Pokemon Sun and Moon), it will likely take you a while. I found a way to do it that does not require you to waste very many items or sacrifice too many pokemon.
Simply put, just get a Sabeleye. They can be found via SOS in Ten Carat Hill (better, since Necrozma is there too) or Vast Poni Canyon. You find a Carbink, then they will eventually call for Sableye. IT DOES NOT MATTER WHAT LEVEL THE SABLEYE IS. The one i used for this is lvl 12 (actually leveled up to 20 after catching Necrozma).
The point is that Necrozma only knows two damaging moves: Wring Out (special Normal type) and Prismatic Lazer (special Psychic type). Sableye, being Ghost/Dark, is immune to both. It also has access to Night Shade (will be known if you catch the low level Ten Carat Hill one), so you can take down Necrozma's HP as much as you'd like without Iron Defense Ruining things.
My strategy was to lead with a Hasty Espeon, then switch to Snow Warning Ninetales (speeds up the HP wear down), then switch to Sableye, then use Night Shade until Necrozma's HP was barely a sliver. Throw Beast Balls until sucessful. It honestly does not even take that long if you turn battle animations off.
Only danger is if Necrozma runs out of PP and begins to Struggle. This didn't cause any issues for me, but it could be pretty easily combatted by giving your Sableye a Leppa Berry and using Trick (egg move from Kadabra line or Mr. Mime) to get it on Necrozma. That will at least give you some warning that it will being struggling soon.
You can swap to a Spore Smeargle if you want, but i found the switch to be too unreliable and the Sleep did not really help or last long enough to be useful.
If you are annoyed with trying to encounter Necrozma, just make sure your Synchronize user at the front of your party (mine was Espeon) is between levels 14 - 74. Needs to be above 14 so you can use a repel to not deal with other spawns, needs to be below 74 or Necrozma will get repelled away too.
Also note that Necrozma is shiny locked (according to other posts on reddit), so it is not worth SRing for that.
Proof that it works:
Good luck and let me know if anything I've stated is incorrect!