Haven't played this for some time, but I'd say that every time you see shiny you get it (if you just kill it first). You can notice it from it's different colors or when you get it, it's name is blue (as normal is white and one with ability has red). I have two Shiny Rattatas, one from password, other one just after putting password, I said that now I can find one from here and after 30 seconds there were shiny Rattata hopping towards me :D
(Go and see page 3 and you can see my shinys and game information. I always play with my brother and sister so we can go fast through the stage with killing everyone. Haven't played for a while, I'm still in Battle Royale EX 4. Have to start playing again sometime.)