For the Shiny Yveltal, deposit a Gastly named "Hades" and look for a lvl 91-100 Yveltal
For the Shiny Xerneas, deposit a Gastly named "Gaia" and look for a lvl 91-100 Xerneas

Yveltal proof: https://imgur.com/a/K8H82fQ
Xerneas proof: https://imgur.com/a/pkc3egF

Yveltal set:                           Xerneas set:

Yveltal @ Life Orb                     Xerneas @ Power Herb
Ability: Dark Aura                     Ability: Fairy Aura
EVs: 4 Atk / 252 SpA / 252 Spe         EVs: 172 Def / 252 SpA / 84 Spe
Naive Nature                           Modest Nature
- Dark Pulse                           - Geomancy
- Oblivion Wing                        - Moonblast
- Taunt                                - Thunder
- Sucker Punch                         - Hidden Power Fire