The Distortion World is an alternate dimension which houses the Legendary Pokémon Giratina.
Players who have experienced Pokémon Platinum Version firsthand should recognize that this Distortion World is in fact meant to be a replication of the Distortion World featured in Platinum. However, while Zeta/Omicron's Distortion World is a replica, it also lacks several features seen in the Distortion World featured in Platinum Version, namely those made possible by the Nintendo DS's 3D capabilities.
The player must navigate the Distortion World by following the path of rocks floating in mid-air which, when contacted via the correct keyboard direction, causes the player to hop across until the next destination is reached. The player must continue this process and work their way southeast until the platform where Giratina resides is reached.
Because the Distortion World is Giratina's natural habitat, the player will face Giratina in its Origin Forme, meaning that its offensive capabilities will be much higher. To allow the player to return Giratina to its "true" form outside of the Distortion World, Giratina will come equipped with a Griseous Orb when captured. Giratina is encountered at level 50.
TIP: Make sure to save before interacting with Giratina, as it will not appear again if it faints in battle.