These are the methods of getting a Shiny Pokémon in Pokémon Black and White 2:
In the wild: You have a 1/8192 chance of getting a Shiny Pokémon in the wild in Generation V.
Nature Preserve: As a reward for seeing every non-event Pokémon in the New Unova Pokédex, the player can receive a Permit that allows them to travel to the Nature Preserve, where they can encounter a level 60 Shiny Haxorus.
Black Tower/White Treehollow: After defeating Benga in the Black Tower (B2) or White Treehollow (W2), he will give the player a level 5 Shiny Gible (B2) or Shiny Dratini (W2.)
Breeding/Masuda Method: The Masuda Method multiplies the chance of hatching a Shiny Pokémon by 6 (to 3/4096 or about 1/1365) in Generation V. It occurs whenever Pokémon of differing real-world geographical origin are bred.
Shiny Charm: As an additional reward for catching every single non-event Pokémon in the National Pokédex, the player can receive the Shiny Charm from Professor Juniper. Having this item in the Bag increases the chance of obtaining a Shiny Pokémon by a flat 2/8192, resulting in a 3/8192 chance (about 1/2731) of finding one normally (an effectively tripled chance) and an 8/8192 chance (1/1024) of hatching one through the Masuda method.
Soft Resetting: This involves pressing certain buttons on the game system to reload the game from the start-up screen. To Soft Reset press and hold L, R, Start, and Select.
Methods which you could obtain Shiny Pokémon but no longer can:
Pokémon Event: There are no longer Pokémon Events for Pokémon B/W/B2/W2.