Must have the same pokemon as a Gym Leader from any region
The problem is that most gym leaders have 3 or fewer Pokemon. Now if we included the Elite 4... Which reminds me, I almost have Cynthia's team in Diamond...
Some more challenges:
The Damage-Only Challenge
All of the attacks on your Pokemon must do damage, and cannot have any added effects (status problems, stat reduction, switch prevention, etc.) Recharge attacks like Hyper Beam and multi-turn attacks like Rollout and Outrage can still be used, but no Uproar because it prevents sleep, and no U-Turn.
The Variety Challenge
No two Pokemon on your team can have the same type or attack. For example, you can't have two Ghost Pokemon on your team, nor can you have two Pokemon with Earthquake.
The No-Item Challenge:
You cannot use or make your Pokemon hold items during a battle with a gym leader, Elite Four member, Galactic admin, or your rival. Also, you cannot use items between Elite Four battles.
The Anime Challenge
You may only use Pokemon that were used by a character in the anime who has appeared in at least three episodes (or is a gym leader). Before you get your sixth badge, make sure all your Pokemon know only attacks they have been told to use in the anime by that trainer.
For this challenge, it helps to nickname the Pokemon after its trainer in the anime, or to keep a list of which trainer each Pokemon belongs to somewhere. This challenge can be interpreted as a way to control the anime characters' Pokemon!
The Random Challenge
Use a random number generator to pick six numbers between 1 and 200. The numbers refer to the Pokemon's Sinnoh Dex number. (For games other than D/P, refer to their own dexes.) Those six Pokemon are your team. (It's possible to get duplicates of a Pokemon species.) If the Pokemon is a stage 2 like Poliwhirl, you may capture it as a Poliwag, but you can't evolve it after it has become a Poliwhirl. If the Pokemon is unobtainable on your game before facing the Elite Four (like Feebas), either cheat/trade to obtain it or pick another number.
In this challenge, you may not catch any Pokemon other than those on your team. However, there are exceptions:
-Your starter. Keep your starter until you catch one of the Pokemon on your team; when you do that, release the starter. (Unless the starter is or evolves to one of the Pokemon you randomly picked.)
-If only the evolved form of the Pokemon you want to catch is obtainable, you may catch the Pokemon necessary to breed one. Release those Pokemon once the egg hatches. (This is useful if one of your random Pokemon is Happiny or something. Keep in mind Pichu and Cleffa can be caught in the wild in D/P.)