Ugh, looks like I made a mistake again. Sorry, Dimidium, Jynx would actually have been right if Fake Out actually did 25%, but it was supposed to be more like 50% (which I've changed in the original riddle post now). But yah, now I can say Slack King actually has the first half correct for mine.
B is easy if you know what Z is, but I guess Z is somewhat hard to get without knowing what A is.
EDIT: OK I think I got it all now.
Trainer1 sent out Dialga
Trainer2 sent out Palkia
Dialga's exerting its pressure.
Palkia's exerting its pressure.
Palkia used Avalanche.
Dialga lost 15% of its health
Dialga used Trick Room
Dialga twisted the dimensions.
Dialga used Flash Cannon
It's not very effective...
Palkia lost 19% of its health
Palkia used Trick Room
The dimensions restored to normal.
Palkia used Flamethrower
Dialga lost 33% of its health
Dialga is burnt!
Dialga used sandstorm.
A sandstorm is brewing.
The sandstorm rages.
Palkia is buffeted by the sandstorm.
Palkia lost 6% of its health
Dialga is hurt from its burn.
Dialga lost 13% of its health
Dialga used Twister
It's super effective!
Palkia lost 39% of its health
Palkia used Avalanche.
Dialga lost 31% of its health
The sandstorm rages.
Palkia is buffeted by the sandstorm.
Palkia lost 6% of its health
Dialga is hurt from its burn.
Dialga lost 13% of its health
Palkia used Aqua Tail
It's not very effective...
Dialga lost 2% of its health
Dialga fainted
So basically first thing I did was noting that Pokemon1 resisted water and was neutral to fire and knew Flash Cannon. That leaves 2 choices: Empoleon & Dialga. Pokemon2 had Flamethrower & Aqua Tail. Only Palkia, Dragonite (and its preevolutions) and Smeargle could learn those, but only Palkia resists Flash Cannon. Then I found that Dialga Twister did max of 39% to Palkia, so I went with that. Dialga was losing 13% every turn after Flamethrower, which means it must have got burnt. Likewise, Palkia was losing 6% every turn, which means Dialga must have used sandstorm. Trick Room ... was pretty obvious since they both moved last when they used it, and Palkia should be faster, which means that's the only thing that fits for those first 2 turns. "A" did 15% one turn and 31% the other, ... which made it a pretty simple guess that it's avalanche, and lo and behold the damage calculation gives 15% and 30%... not sure why it was 31% though.