I'm assuming you already know about the Synchronise ability and how it affects natures.
A faster way to determine the IVs is simply to save your game before the encounter, catch Yveltal, keep it in your party, and then during the battle with Lysandre, check its stats with the summary screen. Put these stats into an IV checker and it will put out the possible IVs it can have! Then, if the IVs are bad, simply soft reset and try again!
There are ways to speed this up even more, avoiding even the catching step if the yveltal is bad. First, set up your party to look like this:
- Your synchroniser at the front of the party, fainted (the synchronise effect will still work!)
- A pokemon that knows Final Gambit, with one HP less than the maximum Yveltal would have with 31 IVs in HP. Make sure it outspeeds Yveltal - give it a Choice Scarf if you have one.
- A pokemon that knows a status move such as Thunder Wave with one speed less than Yveltal would have with the nature you want and 31 IVs in Speed. (Make sure it doesn't have Iron Barbs, Rough Skin, Flame Body, or Poison Point, as you don't want yveltal to accidentally get burnt, poisoned, or take extra damage)
- Any pokemon
- Any pokemon
- An empty slot to avoid the "do you want to keep yveltal or send it to your PC?" question after you catch it
Here is what you do when you encounter the Yveltal:
- Use Final Gambit. If yveltal survives, it has a perfect HP IV, continue to step 2. If it faints, it is not perfect so you should immediately soft-reset.
- Send out your pokemon in slot #3 above.
- Use your status move. If Yveltal outspeeds, it either has a perfect speed IV or it won a speed tie with a slightly-imperfect speed IV, so continue to step 4. If your pokemon goes first, immediately soft-reset.
- Catch Yveltal and continue to battle with Lysandre.
- Check Yveltal's stats and see what its other IVs are.
I used this method when soft-resetting to catch perfect legendaries in ORAS, and it helped speed things up a lot!