I have a shiny palkia with telepathy. Is it real?
Unfortunately no it's hacked.
The Shiny Dialga, Palkia and Giratina distributions that ZekromMaster mentioned in his answer all had the Pressure Ability, you could not get them with Telepathy as their Ability.
(Scroll to see Shiny Palkia and Shiny Dialga)
The only Dialga, Palkia and Giratina ever to be released with their Hidden Abilities was from the Pokémon Dream Radar app.
Source: http://bulbapedia.bulbagarden.net/wiki/List_of_Pokémon_with_released_Hidden_Abilities_(Generation_V) (Ctrl + F, then type in Giratina)
With that being said you cannot get Shiny Pokémon from the Pokémon Dream Radar.
Source: DB Answer and Here.
Because you cannot get Shiny Pokémon from the Pokémon Dream Radar, a Dialga, Palkia or Giratina cannot legitimately be both Shiny and have it's Hidden Ability.
Hope I helped :)
(At least you still have the Shiny Latios that I give you)