in gen 6 (x and y) you can easily "chain fish" and get a shiny pokemon fairly easily. it is not the same in BW2, unfortunately. you'll need to get the shiny charm by obtaining all the pokemon in the game (excluding the four event pokemon). then go to professor juniper and collect the shiny charm. this increases your odds from 1/8172 to 1/2724 i think. then, go into doubles grass and keep walking around. doubles grass basically has two opportunities to get pokemon in one battle, so the 1/2724 rule applies to both pokemon. that is really the only thing, other than the Masuda Method, that you can do to find wild or bred shinies.
there are a few in game shiny pokemon. beat Benga in the White Treehollow or Black City to obtain the shiny Gible or Dratini. I think if you breed with a shiny pokemon, it increases your odds of getting another one. But I am not sure about that.
also, if you just SEE all the pokemon in the game, you can talk to professor juniper and she'll give you the Permit, allowing access to the Nature Preserve, a special area in the game that can only be reached by plane in Mistralton. There, in the center of the Preserve, you'll find a shiny Level 60 Haxorus.
That is about it in BW2, I think. In other games there are more ways to get shiny pokemon, though. Unfortunately, if you do not have access to both Black and White Version 2, you cannot do this, as there are certain Pokemon like Vullaby and Rufflet that can only be found in their respective games.
I hope this helped!