@ Sceptile: You're basically thinking of the "First Come, First Served" Challenge
@ Gymno: I don't know of any existing Challenge like that, other than AceDragonite pointing his finger at me to complete it.
@ Timbjerr: There isn't a challenge like that, although there is a Gym/Elite Four Challenge, where you have to use Pokemon the Elite Four uses.
@ Sydian #1: Right now, I'm doing a Gym disadvantage Challenge, about to start an anime team challenge (Ash in RBY), and Ultimate Ghost Monotype (I'm stuck at Wake in Pt). I've also signed up for Random, Alphabet, and 3rd Gen Duo, although am not currently working on them.
@ Sydian #2: My favorite challenges are monotypes I think. I really like most challenges as long as its not too easy, or any challenge on RBY because its too easy for me. I can run through any challenge on RBY no matter the team in usually 1:30, so those challenges are quick. But monotypes are my favorite.