Paint cracking and leaving a snakeskin-like effect can have a number of causes.
- poor adhesion to the surface, leading to cracking from shrinkage of the paint as it dries. May be caused by surface contaminants (oily residue from your skin etc), over-thinning of paint (so much that the paint's binder is degraded)
- if a primer coat was used but not allowed to cure fully before overcoating with the top coat, the different layers drying at different rates may cause cracking. Allow the primer coat to cure fully before overpainting. Paint in very light coats and allow to cure before overcoating.
- If the paint was applied too thickly the outer layer may be dry, but may crack due to shrinkage of the inner layer as it dries. Paint in very light coats and allow to cure before overcoating.
In my experience, this sort of cracking happens more frequently using gloss acrylics (I've seen this with Tamiya and Gunze gloss acrylics). I've not seen it happen with flat paints.
As far as I am aware, there is no way to fix this other than stripping the paint and repainting. Simply overpainting will fill the cracks, yes, but will also add thickness to the rest of the paint, meaning that the cracks will still be noticeable.