i am very sorry but you cant get him/her on leaf green.
Piplup does not exist in Pokemon LeafGreen or FireRed.
The short answer, you don't. The long answer, Piplup is a Generation IV Pokemon, which means it was only introduced in Pokemon Diamond and Pearl. Pokemon Red is Generation I, so at the time, Piplup didn't exist.
You cannot capture miltank in leafgreen only Pokemon colosseum can.
cheating
your rival would pick a water type Pokemon which is a squirtle
use a master ball on it
Sadly, You can't catch Oddish in LeafGreen. You can need to trade it from FireRed.
Its not possible to capture any hoenn Pokemon in leafgreen if you want a roserade trade one from ruby, sapphire or emerald to leafgreen.
If you didn't choose it as a starter, you cannot get Piplup throughout the game at all, unless you have cheats/a hacked game, or you get a friend to trade one to you.
Only firered can capture qwilfish trade one from firered to leafgreen.
capture zapdos with an ultra ball
Piplup is a Water type pokemon.