You wanna bred all 4 different kangaroos and their color variants for this one, by doing this you get also the other Australian bred achievement for breeding all the kinds of Australian animals.
You can get this in Free or Challenge mode, i recommend doing it in Free mode because you have unlimited money to spend etc..
Build 4 big/medium Australian outback's.
Adopt in every outback a different variant of Kangaroos, if you build a big outback(10max) you wanna buy 3male and 3females, and medium outback(6max) 2male 2female.
Make your animals happy by buying food, wash stations and something to play with, it need to be for kangaroos (3stars), hiring zoo keepers will help also.
Then build a breeding facility and employ 4 people, then assign them to the 4 Australian outback's.
Then just wait..
If you don't get a color variant right away you can sell or donate it, or release 2 adults in the wild, 1male 1 female ofcourse..