You could just battle normally in the Z-A Royale, but here's a somewhat silly strategy for if you only care about EXP and not money or challenge tickets:
Find a trainer in the Z-A Royale that leads with a strong Pokemon that you can easily defeat. The trainers who lead by immediately using Explosion or Self-Destruct work for this as long as you have a way of avoiding the attack. When their lead Pokemon faints and you gain experience, physically run away from them and the battle will end. You can then reapproach them and faint their lead Pokemon again, repeating the process as many times as you want since they'll never disappear as long as you never complete the battle. It's best to do this in a spacious corridor away from other trainers since that makes it easiest to leave and restart the battle.
Once you've unlocked the Infinite Z-A Royale, you get Exp. Candy rewards for winning promotion battles, so playing normally can be more useful for leveling up Pokemon who have reached level 70+ and aren't growing as quickly from the Royale trainers anymore. The reward depends on your win streak (source):
- 1-10 wins = 10 pieces of Exp. Candy M
- 11-20 wins = 15 pieces of Exp. Candy M
- 21-40 wins = 6 pieces of Exp. Candy L
- 41-60 wins = 7 pieces of Exp. Candy L
- 61-80 wins = 8 pieces of Exp. Candy L
- 81-100 wins = 9 pieces of Exp. Candy L
- 101+ wins = 10 pieces of Exp. Candy L
Another strategy is to trade in Mega Shards for Exp. Candy at Quasartico Inc. The larger sizes aren't available right away, but the ratio of experience and price is balanced, so you could just buy more of the S size.
- 8 shards = Exp. Candy S
- 30 shards = Exp. Candy M
- 100 shards = Exp. Candy L
If you've accumulated over 20 wins in the Infinite Z-A Royale, you also unlock the ability to battle Jacinthe at Hotel Richissime as many times as you want. She has a full team of level 73-75 Pokemon, being among the strongest rematchable trainers, which can be helpful if the Pokemon you want to level up are also in the higher levels.
