X and Y
No gym leaders in Kalos use Mega Evolution throughout the story (or during rematches) except for Korrina, who uses Mega Lucario in one special battle that is unrelated to her gym battle.
No Elite 4 members in Kalos use Mega Evolution throughout the story or during rematches.
- Champion Diantha uses Mega Gardevoir.
- Serena/Calem use Mega Absol
- Lysandre uses Mega Gyarados in his 3rd and 4th battle
Omega Ruby and Alpha Sapphire
No gym leaders in ORAS use Mega Evolution throughout the story or during rematches.
During the main story, the Hoenn Elite 4 does not use Mega Evolution. However, during their rematches:
- Sydney uses Mega Absol
- Glacia uses Mega Glalie
- Phoebe uses Mega Sableye
- Drake uses Mega Salamence
- Champion Steven Stone uses Mega Metagross
- Maxie uses Mega Camerupt
- Archie uses Mega Sharpedo
- May/Brendan use either Mega Swampert/Sceptile/Blaziken
- Wally uses Mega Gallade
- Zinnia uses Mega Salamence
Sun and Moon
No battles outside of the post-game include Mega Evolution. However, you can look at this link for trainers that use Mega Evolution in the Battle Tree and other areas.
Ultra Sun and Ultra Moon
No battles outside of the post-game include Mega Evolution. I believe the same link above covers the same trainers who use Mega Evolution in the Battle Tree and other post-game areas.