Take a Tentacool, name it "knockout". It doesn't have to KO or solo anything, but the more you kill with it, the better. A "major pokemon" is one that belongs to either Maxie, Archie, a Gym Leader, or an Elite Four/Champion.
Once you catch it, you may not use more than three moveslots, and you may not use a move with base power greater than 50, and the sum of the Base Powers of the moves may not exceed 100.
Once you solo one major pokemon with it, you may use moves with up to 60 base power, and the base power sum rises to 140.
Once you solo two major pokemon with it, you may use the fourth moveslot
Once you solo three major pokemon with it, you may use moves with 70 base power, and the sum rises to 180
Once you solo five major pokemon with it, you may evolve it
Once you solo eight major pokemon with it, you may use moves with up to 100 base power.
Once you solo thirteen major pokemon with it, the sum rises to 300.
You may NOT soft reset to re-battle a leader if it dies, so if you screw up against some easy solos, tough shit.
You do not have to fulfill any of those challenges, but you WANT to, don't you???