How did VLT's adaptive optics obtain this resolution for Neptune? Is it really working in visible wavelengths?
It is an image taken with the new narrow field mode of the MUSE instrument using the GALACSI Adaptive optics module on a single (UT4) VLT telescope using laser guide stars.

I am having a great deal of difficulty (e.g. from this press release) in working out at what wavelength(s) this image was taken. I do not believe that the AO system is working at blue wavelengths and therefore the comparison with HST (which certainly does) is somewhat misleading. I think (from ESO's own instrumentation pages) that the MUSE narrow field mode has zero efficiency at blue wavelengths and the description of GALACSI only talks about AO correction approaching diffraction limited images at 650 nm (i.e. red wavelengths).

The captioning to the press release images found here suggest that the shortest wavelengths used in this false-colour image were 550nm and that most of the detail you see is coming from redder wavelengths (600-920nm).