You can find Cobalion in Mistralton Cave and once you do. You might want to save and soft reset every time if it isn't. It is hard to find though.
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you catch cobalion
Leave and return to the cave and Cobalion will have returned. So then you may capture it. I suggest Timer Balls.
Pinwheel forest, after catching cobalion in the guidance chamber.
There are a total of eight Legendary pokemon legitimately obtainable in White alone: Victini(Liberty Pass), Kyurem, Zekrom, Thundurus, Landorus, Cobalion, Terrakion, and Virizion.
No they programmed the game so you can't catch shiny victini, reshiram, and zekrom. All other pokemon can be found shiny.