The first issue can be that perhaps all your pets aren't level 25? If that's not the case, I've heard of a few bug reports from players not getting credit on a fight. You can try restarting the game and doing the fight again, but if the bug persists, I'd put in a bug report and choose a different fight to complete the Flying achievement.
This strat has a little bit of RNG. I had a run of bad luck with no crits in turns 1-4 on my first pet which meant Eighty Eight didn't die on turn 4 to Ravage like the strat implies. Other than that, solid strat! My Ikky consistently finished the fight on its turn 5.