The Elite Four wasn't too bad for me. Spamming items allowed me to pull through my first time.
Red I beat with a team consisting of a Level 56 Gliscor, 52 Snorlax, 61 Gyarados, 24 Geodude, 26 Krabby, and a 16 Farfetch'd. How could I have won, you may ask? Simple. Strategy. ;]
Gliscor easily kills off Pikachu with Earthquake. Then, I use Snorlax against Lapras to try to drain it's Blizzard PP and/or paralyze it. Finally, I bring in Gyarados, try to set up 6 Dragon Dances without hax getting me, and I proceed to try to sweep his team. The only other speedbumps are Snorlax (Who OHKO's with Giga Impact), which I flinched to death, and Blastoise, who I stalled out of Blizzards and swept.
Pretty epic win if I do say so myself.