You could probably get decent mist by using the mist pass in compositing. That has basically no impact on the render time.
Alternatively, do use a box with real volume fog, but use an emissive node as volume instead of the more fancy types, it makes a shadeless fog and is faster.
Both of those options will give a similar result (with the difference that the real emissive fog will add a bit to the lighting). Both will give a flat fog without any real shading in it, but that’s still much better than no fog at all, especially in a scene like this one that really needs it.
On top of using one of those tricks to make fog, you could also add some clusters of planes with faint transparent cloud textures to make some denser cloudy areas. This is cheaper than real volume fog, as long as it’s used sparingly to make a few clouds and not to cover the entire scene everywhere.
If you want light beams, they could be faked with meshes (again, using emissive as volume) since the fake fog won’t create them.
Notice how the movie’s lighting is placed strategically. There is only one light beam that adds golden light where you are supposed to look, the rest of the scene is a darker, ambient blue.
It’s not just the lighting either, the image composition and the way objects are placed are also very important.
Note that the objects around the characters aren’t random. Everything is pointing towards the characters with a bunch of lines funneling the viewer’s eye in their direction. The light beams, the vines, the bark on the right, even a bunch of plants all over the image are creating lines converging to the center of the image. The areas that are less important to look at either have big masses of foliage/bark that block the view or are faded in the fog in the distance.
I am also going to point out how uneven the movie landscape is. The ground seems slanted and difficult to navigate with those massive diagonal roots. There are multiple areas that have a unique type of plant or a visual feature that’s nowhere else in the image.