These are almost certainly moulded thermoplastic rather than cast resin — mass-produced toys use the cheap high-volume process — and that is good news, because thermoplastic polishes beautifully.
The approach is the same one used for scratched watch crystals and headlight lenses: progressive abrasion, from coarse enough to remove the damage down to fine enough to restore gloss.
- Clean thoroughly first. Polishing dirt into the surface adds scratches.
- If there are real nicks, start with a very fine wet abrasive paper — the sort sold for finishing paint — used wet, with light pressure, in small circles.
- Step down through progressively finer grades. Do not skip grades; each one is removing the scratches left by the previous one, and skipping leaves marks the finer grade cannot reach.
- Finish with plastic polish or a fine automotive compound on a soft cloth.
The two rules that matter: keep it wet, and keep it cool. Friction melts thermoplastic, and a melted spot is much harder to fix than a scratch.