Microdermabrasion is not a standard treatment for melasma. Rather, it would be better to try different bleaching creams, specifically Triluma, to try to lighten the area. Sometimes laser will work, but studies have shown that melasma will recur after laser in most cases, so at most, it is temporary relief. Contant use of a bleaching cream + laser (if desired) may be a great starting point.
Also, Cosmelan is an excellent treatment. It is meant to be a once a year treatment, but you can repeat it in 4-6 months if the results are good, but not perfect. Other options for melasma include repeated glycolic peels. Theoretically, deeper peels would work, but I would worry about it coming back worse.
The standard rules apply: birth control and pregnancy will worsen melasma. Those two and sun exposure will prevent any treatment from working.
Hope this helps!