Heh, well, there is a mode called firefight where you fight till you die and the enemies get progressively stronger. Bout the hardest thing you can do. In Halo 3 ODST there was a challenge called "Endure" which required you to be on 4 player co-op and survive 4 rounds of firefight on the second hardest difficulty. I did it twice. Took around 2 hours each time, and was by far one of the hardest things I have ever done in my life.
My first time through I was all badass and won the challenge for my team. We had three enemies to go, enemies with one hit kill weapons, and everyone died except for me. I killed two of them with hits from their own weapons, but ran out of ammo and had to melee the last one to death. Needless to say my friends loved me after that.
Anyway, no I don`t think I`d ever try a no kill run.