It is possible it is legitimate. You are able to get a Level 1 Giratina if you take an Event Arceus to the Sinjoh Ruins in HeartGold or SoulSilver. The Giratina will appear in its Origin Form, but this isn't indicative at all, as it changes forms when you take the Griseous Orb away from it. At level 1 I believe its move set should just be Dragon Breath and Scary Face, unless it has been taught TMs or Move Tutor moves.
With that having been said, it is possible that it is legitimate, but it is not particularly likely, as you need an Event Arceus in Gen IV to get it, and these obviously aren't being distributed any more. On the other hand, the fact that it is not shiny may suggest that it is legit, as most hackers will make their Pokemon shiny.
Hope this helped.