The main question would be about the accuracy of the emulation. I know there have been phone apps in the past that don't meet the threshold of accurate enough emulation, but I don't have any knowledge about this one in particular.

Another thing that can contribute to this behavior (this is especially true on the Jaquio fight, because you're also trying to slash him while you're near the wall) is that you could be holding down the slash button while trying to jump off of the wall. That could happen after you spin that gremlin in 5-2, too or (I'm guessing this is where you were) after slashing the karate guy before you climb up to the dragon cannons. You have to be hitting directly away from the wall, jump, and nothing else. I use Nestopia and have used FCEUX a little, and I don't think it's likely to be an emulator problem. Similarly, I have used iBuffalo USB controllers, and they were fine too (assuming the d-pads aren't broken or something).