From Halopedia, the Halo wiki
Play through the level normally until you get to the area outside after you have exited the second underwater elevator. Kill all the enemies, and wait for the Pelican to arrive. When the pilot says, "This is my last run, Chief, I'm nearly out of fuel.", look for a small bulge of land to the far left of the hill where the Elites were. Jump on this ledge, and when the Pelican has lowered near to the ground, jump on top of it. When the Pelican takes off, jump off to the right of the direction the Pelican is flying. Turn right and walk up the left side of the mountain. On the mountain you will be so high that some parts of the level will not be visible, as the level is split up into loading points that must be triggered for the level to appear. Also, in other areas, nothing is programmed on the map and there is a black space, because that area wasn't intended to be seen in regular gameplay.
There is a second way to get outside of this level, but you will need the Sputnik skull. At the start of the level, go up the ramp to your left and there should be a ledge near the wall. Grenade jump up there. Once up there, grenade jump again and you should be on the roof and you can take the walkway back through to the mountains. You can explore the levels mountains like in Delta Halo but it will eventually get boring walking across the mountain because you don't have a Ghost with you to drive.
Things to do
From here you can explore the side of the level across from the Delta Halo Vacation without walking all the way around, which takes several attempts culminating at several hours of walking, after which you will most likely not wish to explore. If you want to, you can go to the edge of the level by simply going to either side of the mountain until you reach a gray wall at the very end. Also, if you go down to the left before the mountain, you can go down to a beach of sorts and even go under water.
At any point you can return to the level; simply backtrack carefully down the slope and jump of the small ledge near the ruins where the gondola that takes you to Regret's temple is located.