If they can get a few days of good weather on their side, the team hopes to first make an unmanned 11km dive with the sub, to check it works properly at this deepest of ocean depths - and then it will be time for James Cameron to enter the craft and take the reins.
The craft, which is housed on the ship's deck in a large, air-conditioned hangar, is bright green, weighs 11 tonnes and is more than 7m (23ft) long.
Once in the ocean, it flips on its end, and descends vertically through the water column.
The compartment in which Mr Cameron will spend his nine-hour dive is tiny: a thick, metal sphere with an internal diameter of just 109cm (43in). He will be curled up inside, unable to stretch his arms or legs.
The rest of the sub is made from specially designed syntactic foam, similar to the sort of thing a surf board is made from.
It is packed full of 3D cameras and huge lighting systems so that the director can capture the excitement of the voyage all the way to the bottom.
The director plans to release a documentary with footage captured on his dives - but he also has science in mind.
The sub, which has been financed by Mr Cameron along with National Geographic and Rolex, is fitted with robotic arms that can bring sediment, rocks and samples of deep-sea flora and fauna back up to the surface.
When he attempts the Mariana dive, a science team, headed up by Doug Bartlett from the Scripps Institute, will be dropping a lander - also kitted out with 3D cameras - which is baited to attract any passing life.
Mr Cameron says: "Every single dive, I'm going to see something no-one's ever seen before.
"I'm going to do my best to image it, light it properly, bring it back in 3D - grab samples if I can, grab rocks if I can.
"We are there to do science, but we are also there to take the average person who only imagines these things and show them what it is really like."
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