Simply catch a total of 200 carp on your profile. This can be any species, and can include DLC.
This includes Common, Leather, Mirror, Ghost, Koi and Siamese.
The fastest place to catch carp is Talon Fisheries (DLC) in the Koi lake, or without DLC in Grand Union canal.
Depending on where you fish, the bait will change. But if you stick between size 8-12 hooks and use boilies, you will always catch carp wherever you are.