Pet Battle World Quests are drawing some attention, not just from collectors and battlers, but also from players looking to earn reputation and artifact power.
For a collector/battler, most of the quests will be straight forward. With a large enough collection, the fights shouldn't be a problem.
However, for someone just getting into Pet Battles or is only doing these new quests for rep/AP reward, the encounters may not be as simple.
Since I'm not one to create guides/strats for fights, here's a website that has some team ideas for Legion Pet Battle World Quests: Xu-Fu's Pet Battle Strategies
Many of the pets used do not need to be a specific breed, and they're relatively "easy" to collect.
For more advanced pet battlers, the same website also has suggestions for Family Familiar strats. It's a great resource if you get stumped on a fight. :)