Thanks for the comment! The trick with this one is that most of the visuals are actually written in code rather than sprites or spritemaps. So each parallax layer is vertical lines drawn each frame with the height given by a wave function which is re-evaluated every frame based on the distance of the "camera". Not gonna lie, it took a good chunk of the second day to figure it all out but I can see myself using this technique a lot so it's time well spent.
I learned that devs love to use "Perlin noise" for this kind of thing, but I think it's a bit much for the PICO-8 processing limits (maybe it would be fine here in 1D, didn't try). This cart literally just uses two sine waves: a low-amplitude, high-frequency "ruggedness" function on top of a low-frequency, high-amplitude function (for the overall mountain shape). Then each layer just uses slightly different amplitude and frequency values to feel visually distinct and of course a different scroll speed to help sell the illusion of depth.
I'm glad you noticed the wobbly pixels on the most distant layer! For that, I just forced everything to use half the effective resolution by halving, rounding, and then doubling again (so the height always jumps 2 pixels at a time). Basically, lower res = "blurry" = "further away"; it's crazy what we can trick our brains into believing from such simple images! I should have done something similar for the x-axis, but I guess I got sidetracked.