Having played a tonne of pet battles now, and really got into the system in general, I wanted to share a few tips for those starting out.
- Know your types
This is vital for anyone looking to succeed at the battles. You don't want to be pulling out a pet at the wrong time against something that can annhilate you. There are various type charts available online, and the UI gives enough information as standard to show you what is weak and strong against your target. Make sure to read those tooltips.
Having a team of all Murlocs may look cute, but you aren't going to get far when you go up against a pet that's strong against humanoids. Use pets that compliment each other well, ensuring that at least one of your team can self heal to a considerable amount (Frogs and Crabs are good interveners here).
- Take a few risks
Sometimes a battle can be on the wire, and it can be decided on the luck of a lucky dodge or miss. Don't be afraid to chance your last few HP on what could be a winning blow. There can only be one (except in the case of a draw) winner, and sometimes the victor is the one that rolls a 20. Remember though that they can always backfire.
- Moar DoT's!
Some pets have moderately powerful DoT's, and can be used when you are up against a powerful tanking/healer hybrid. Sometimes you will not be able to outdamage your opponents self heals, so DoT's can help nulify them. A good starter would be to use the Fel Flame's Flame Breath, then Conflagerate, then Immolate, to usually one shot your opponent, while nullifying their healing. Switching into other pets that have persistant DoT's can usually bring you a win.
- Persistance brings Victory!
When you are out in the wild hunting for those elusives, keep trying till you get the blue variant. The tiny boost in stats can decide a win a turn early as well as the ability to go first. Using the "PetBattleQualityGlow" addon shows you the rarity of your target when capturing pets, allowing you to run from those battles you don't want to waste time on.
- Test out all kinds of combinations
Some moves work very well in tandem with others, for example Mini Tyrael's Stun goes well with the turn charge required for his Holy Charge. Using Burrow on a target that has already Burrowed allows you to attack them underground, and the same for Fly. Reflect is a very powerful ability, usable every 5 turns to turn the enemies moves against them, but multi hit moves that attack the entire team can seem powerful, but unless they switch out their low HP pet, are generally weak. Stick with high accuracy, high speed moves, as while they may not do as much damage, you have a better chance to land some.
- Find a Stable Master close to your grind spot
Kind of obvious, but finding a Stable Master close to where you are currently exping (remember always choose targets 2-3 levels higher to maximise your exp gain) allows you to heal up and continue without waiting on the heal timers, or using your bandages up. On that note, try to find a target you are strong against and kill all 3 wild pets with one of yours to get top exp, and level quickly.
- Find out what your passives are
Most passive abilities are only shown in battle, such as healing on every attack, or chance to drop attack power on hit. These passives are insanely powerful, but so far have not seen them documented ingame. Knowing them means you can know your enemy too, and turn the tide of miniature battles in your favor.
- Unlock the Dailies!
Another obvious one, but getting those dailies unlocked mean you can always know the 3 pets you are going up against, and as the trainers offer large amounts of exp, can be good for getting a pet boosted up quickly. Another tip there is if you have high level pets and want to get a low one up quickly, have it as your starter, make it use a move (ones that stop it from dying are a huge boon) and then switch to your main pet to kill the enemy. This way I get 4 levels in the first fight, 3 in the next, and so on. Very quick way to skip out the starter grinds.
Hope some of this is helpful, and I will add to it if people have points to share!