As usual, with these kinds of battle facilities, formulating a winning strategy that applies for all battles is impossible due to the huge variety of opponents that you’re facing. On top of that, you can’t use your own Pokemon, but instead whatever the RNG gives you. Still, here are some general tips that you should keep at the front of your mind.
Build a diverse team.
Despite your options being restricted, especially with your teammates’ Pokemon being locked, you can still work with what you have. Are your team members bringing in Pokemon of a certain strength, such as being good at physically or specially attacking?
Then look at the three Pokemon you can pick from and select the one that is most different. Be sure to consider type diversity as well, and also the moves that they pack. Some Battle Agency Pokemon don’t know a single attacking move, and you don’t want to have three of those.
Pay attention to hold item, moves, and nature.
Looking at the hold item and the moves will tell you fairly quickly what the Pokemon’s role is designed to be. For example, there is a Moltres in the Battle Agency that holds a Power Herb and knows the moves Flame Charge, Aerial Ace, Sky Attack, and Fire Blast. Its nature is Naughty.
From this we can deduce that Moltres is meant to be used as mostly a physical attacker, with Sky Attack being its trump card. Normally Sky Attack requires a turn to charge. However, the Power Herb means that Sky Attack will trigger immediately and can be used to deal heavy damage to a potent threat.
Meanwhile, Flame Charge and Aerial Ace are good standard use moves for a physical attacker. The former raises Speed and the latter never misses. Finally, Fire Blast is a special attack that can punish physically defensive Pokemon that come to try and wall Moltres.
Pay attention to a Pokemon’s moves, nature, and item. That will help you deduce how to maximize its use, and pinpoint weaknesses you can patch up in your other two team members.
Try your best to avoid Pokemon with no attacking moves.
A Regigigas that only knows Confuse Ray, Double Team, Toxic, and Wide Guard is more or less useless. Chances are you’re going to face off a Poison-type Pokemon. Try to get a Pokemon that knows at least one type of attacking move, and if you must settle for a Pokemon with one attacking move bring a team mate that can cover their weakness.
Turn off attack animations!
This is more of a quality of life timesaver than anything but turning off attack animations will save you a ton of time as you take the long road to grade 50. Get out there and win some battles in your cool sunglasses!