There's very little programming involved with the 'animations', just clever usage of engine features - the only relevant script for the lines is a bezier curve script.
The legs are line renderers with the points positioned in such a way that they properly flex when different points attached to the body or feet move relative to one another.
The large tentacle is also a line renderer, the points are initially positioned within a rectangle (ie offset within a parent object) - I can then rotate and scale this parent object to get the 'animations' of the tentacle reaching out.
The human body's slinky-like behaviour is somewhat programmed however, it changes the relative angle of each joint when you move left and right.
The mess I mentioned is how the feet move - they try to move a set distance from the center of the body, but they stop if they reach a low velocity. The body then catches up to a different position depending on which foot is moving (so if you're moving right, while the right foot moves the body won't move, then it catches up, then left foot moves). This is the extremely dumb part, as doing it relative to the body that's also trying to move relative to the feet is what caused all the trouble. Had I used one foot's distance to the other, it would have been much easier.