How to achieve "Acid Burn" saturation?
I have not seen any movie that used any onset technqiuqes for this look. Of course you want the lighting to give away a certain mood to begin with but there are no special filters needed.

For the post production workflow, there is a great plugin for several video tools like After Effects, Premiere and Final Cut from Red Giant called Mojo that makes it extremely easy to achieve and fine tune such an effect. They also offer other tools to achieve specific filmic looks.

If you don't want to use a plugin or simply want to achieve a more "unique look", you can play with contrast and the individual color channels. I recommend using a "Levels" effect not a "contrast" effect, you usually have greater control with that. Then punch the blue channel up a bit and the green channel aswell but not as much. For some scene you may want to work with masks to strengthen the effect in some areas without overdoing it in others.

What can also help even more to achieve the color distortion but is not available in every video editor is to apply a blue (or other color depending on your desired look) layer over your footage with a blend mode like "Overlay" or "Vivid Light" (that's how they are called in Adobe programs) and adjusting the transparency of the color layer. This tints the image nicely in a blueish dark look.
Play around with different blend modes, you can achieve very interesting effects with that technique. Your video software just needs to support blend modes for that.

You also want a very sharp image, thats important for the effect to really shine and have this "harsh" feeling. Applying a very subtle sharpening effect could be benefical.

You can also add a vignette as used in your first set of screenshots.