Method 1 - Play through the level Uprising until you get to the first outdoor area, then proceed and kill the Brutes. Head through until you get to the large area containing a Spectre full of Brutes. Kill the Brutes without destroying the Spectre (make sure you have one or two Ghosts remaining to use). From the entrance to the Spectre area, drive the Ghost up the wall on the right. A bit of nose-wiggling may be required. Park the Ghost in the small corner and then return by jumping onto a tall rock and slide down to get up the second Ghost (this Ghost is not required but it does help).
Then, drive the Spectre up the wall and over the Ghost, make sure the nose goes up and with a bit more nose wiggling you can get it out and onto the mountain.
Method 2 - When exiting the indoor area and approaching where you first grab a Ghost, there is a purple structure right next to where the Chieftain's Ghost will stop, dispatch of the enemies then jump on this structure and jump towards the long rock on your left if you were facing the canyon. From there, there is a small gap between the wall and the tree in front of you, jump in between turn slightly to your left, jump and push forward until you are on top of the rocks.
Method 1 - From here you can drive right around up Uprising and look down on bits of the The Great Journey. If you wish to return, simply drive the Spectre off the edge and back into the level, however, try not to fall from too high as the fall timer will kill you. You can even proceed to the end of the level and jump down the cliff (and die) and see another Arbiter falling from the sky in the ending cinematic of Uprising. This will complete the scenario. This is very amusing during co-op, when two Arbiters fall in front of the real Arbiter.
Method 2 - From here you can turn right and continue down along the entire level, with the rest of the level already loaded but without any AI or vehicles. If you stick to the right, you can make it all the way to the final part of the level where the enemy Wraith is located, it will not have spawned and neither will any of the Brutes or Jackal snipers. The video attached will show you how to jump down to this area safely and complete the level.