True HDR requires multiple bracketed exposures of the same subject... not usually suited to video unless you have a locked-down camera and a static subject, but then I suppose it is doable.
To fake it, I'd suggest first playing with camera contrast and saturation settings until you get something that you like, and then stick to low contrast scenes (I wouldn't for example, shoot outdoors on a sunny day where you would have blown-out highlights along with black shadows that suck up detail).
Then, in post you should be able to do some tweaking (probably proc amp and color correction filters) that will bring the contrast back way up and goose up the saturation a bit.
You might even take the same clip and make two (or more) layers of it... say playing with contrast to bring out detail in the shadows in one later, and details in the highlights in the other... lay them on top of each other and image map them together (maybe a luma key using a third track of the footage but super contrasty to use as a track matte?). That might give some acceptible results.
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