This look is generally called solarization (or solarisation): a partial reversal of tones, originally known from analog darkroom processes.

Based on the community answers, a practical Photoshop approach is:

• Start with a negative/inverted tonal approach rather than applying the effect directly to a normal positive image.
• Use Curves to push tones so some areas begin to reverse in appearance.
• Add a Gradient Map to create the unusual color palette.
• Refine with layers, masks, opacity, and local burn/dodge adjustments to control where the effect appears.

A related way to get a similar look is to begin from a scanned color negative and avoid normal color correction. That can naturally create the strange color shifts and surreal contrast seen in solarized-looking images.

So: search for Photoshop solarization tutorials, but expect to combine inversion/curves, gradient mapping, and selective masking rather than relying on one single filter.