one of the more annoying pets used by the npc tamers is the whispering pandaren spirit's elemental pet. this is because if you bring an aquatic pet to maximize your damage, you simultaneously make yourself vulnerable to its flying damage, which is strong against aquatics. the solution is to use a pet which does aquatic damage, but is not itself an aquatic pet. unfortunately there aren't very many of these pets - water jets not being popular with the scorpion crowd, etc.
i've been using frederick, a rare oily slimeling, and his creeping ooze attack, but this is less than ideal, since if you use it every round you overwrite the damage-over-time component. so i end up weaving it in with non-aquatic attacks. much better is an idea my wife had, that i thought i'd pass along:
turn the tables on them. if you've managed to acquire a pandaren water spirit, level it to 25 and it becomes the ultimate air spirit killer. it's elemental, so it isn't vulnerable to flying attacks, but configured with water jet, dive, and whirlpool, it can blast its opponent with a water attack every round. makes this fight hella lot easier.