I had difficulty with the champion of R/S/E. I'm talking about both champions, Steven in Ruby/Sapphire and Wallace in Emerald. My Pokémon weren't that very strong at that time. Steven's Metagross was hard to beat for sure, and I had trouble with Wallace because his Water-type Pokémon had Ice-type moves, and it would greatly damage Sceptile, my starter.
Other than that, Tate and Liza was also a hard duo to beat, especially in Emerald since they had additional two Pokémon. I hate it when they use a Hyper Potion, and they have two of it!