About desperation moves...

Truth be told, counters aren't really the biggest concern in Brave New World - it's seizure damage. I have thoroughly examined its effects on enemy behavior and can say beyond a shadow of a doubt that periodic damage does not trigger counters (which, now that I think on it, is quite possibly because the game's code considers the source of periodic damage to be the target itself). I lump counter-attacks and desperation attacks in the same category because they behave the same way, as far as my experience goes.

I had, for example, someone defeat Dadaluma in BNW by doing nothing but counter-attacking him. Dadaluma has 25,000 HP but is set to die in the reactive part of his boss script at 10,000 HP remaining. This never happened, and Dadaluma finally died normally (instead of like a boss, as his script would have him do) to a counter-attack.