Guess what? I beat the E4:
My team in the Hall of Fame:




My thoughts about each team member:
Serperior - She carried me through early game, when other members were weak. But I don't think I used her during my E4 battles much. I realized that Grass-Types aren't that good in this game.
Crobat - Second member I got and once again, shined most during early game. I didn't use it during mid game until the E4.
Vaporeon - To be honest, I really didn't use him as Eevee and didn't use it much as Vaporeon, but when I used it, it was awesome.
Cof a grigus - This one surprised me. His wall combined with Will-O-Wisp saved me many, many times.
Sawsbuck - BEST MEMBER OF THIS TEAM! I'm not kidding. There are lots of Pawniards in this game and Sawsbuck was my only Pokemon with Fighting-Type move. With Horn Leech for healing, it was unstoppable.
Bisharp - My last member and the one I used most since I got him. Steel/Dark combination is so good in this game. It got rid of 2 E4 members and was able to stand against Iris for good amount of turns.
And finally, few words about the challenge itself:
I loved it. This team made the game far more harder that expected but it actually was pretty funny. I'll probably check this Challenge once again soon.