I've done this once before and got perfect results. In this case you are lucky because the Pokemon is shiny meaning that its Special, Speed, and Defense IVs are all 10. So by chance can you post what Togetic's HP stat is at and what its Hidden Power is. By finding its Hidden Power type it'll allow us to discard half of the possible Attack IVs that a shiny Pokemon can have. Also from my calculations it has ~18000 points for each DV so I can only assume that the Attack and HP stat will have similar DVs. Since there isn't a Hidden Power checker in the game you'll need to teach him Hidden Power from the TM that is in the north west house in the Lake of Rage. Then you'll have to battle a Pokemon and find out if the Hidden Power is super effective, neutral hit, or not very effective. Doing that will allow you to determine which Hidden Power type you don't have. Then repeat the process with battleing different Pokemon until you narrow down the type. In this case the Hidden Power will be either Dragon or Grass.