Odd wants to apologize to his father, Jeri, who (amongst a laundry list of other things Odd is sorry for) in a roundabout way gave his life so Odd could keep his.

With how awful Odd's self worth can be and with how much of a pedestal he put his dad on, his 'apology' would be something along the lines of:

"I'm so sorry I somehow tricked you into believing my life was somehow worth more than yours."

Mary would want to apologize to her parents for not being able to save them. She was just a kid though, and nobody blames her but herself and especially her parents wouldn't want her feeling like that...but the feeling's still there.

A certain ghost type gym leader, he wants to forgive them because they’ve changed and become a better person, but he just can’t help but still feel angry at them (spoiler: He sorta never does)

Grim and Blake have something in common, they would like to apologize to their sisters. In Grim's case, his older sister and in Blake's to his younger sister (RIP)

Briar would like to apologize to Lysandre for not doing enough for Team Flare. She's always plagued by the 'If I had done a little bit more, it wouldn't have gone wrong' mentality, and is the reason why she pushes herself to the limit nowadays. But she can't apologize to him because he's, well, dead. She wants to apologize for letting him die.

Zephyr desperately wants to apologize to Jean, their last meeting was when he told her of his plans to leave the knights and it didn't go well.

Caporei to Grendam on account of the infamous Kommo-o indecent.

For Wily it's the Darkrai he accidentally helped rope into his dad's experiments.

Andre would apologize to his grandparents for not being around as much as he should have and for keeping secrets from them; he was never able to tell them the kind of work he was doing with Interpol. Unfortunately they both passed away before he could ever say anything

Avian wants to apologise to Barry, during his 'Main Character Syndrome' era in sinnoh they were friends but as Avi grew stronger he grew more distant and apathetic. "I don't hate you, I don't care about you" is one hell of a final line to give to someone who cared about you. He never forgave himself for that

Hm probably to Lance, because Tyler is the type of person to try to do things on his own, they get into arguments about how he needs to ask for help when he needs it, mainly because Tyler wants to step out of Lance's shadow and prove he's strong

Later on, Tyler would learn some humility and learn to ask for help when he can, so when he realized this, he'd want to apologize to Lance. However, with current story stuff they need to do, Tyler hasn't found that chance yet, and he doesn't know if he's ready to confront him yet