Pika Cup: Pokémon can only be between level 15-20.

Petit Cup: Level ranges between 25-30. There is a height requirement though. Height 6'8" limit and weight 44 pounds.

Poké Cup: Only can use 3 Pokémon, levels 50-55. The sum of the Pokémon's levels cannot exceed 155.

Prime Cup: Everything is legal. You can have any level, height, weight, or number of Pokémon. However, your opponents' levels are always 100.