The photo is helpful, but an in-person evaluation is more valuable. In general, there are three reasons why the skin around the eyes can be [or seem] darker:
1. The thin eyelid skin allows the darker muscle underneath to show
2. The hollowness around the eyes can create a shadow effect that exacerbates darkness. This is further amplified if you have some fat prolapsing in the eyelid making a contour irregularity.
3. Skin pigmentation [sometimes from blood products from bruising] If it is blood product pigmentation, it could last months to improve.
Depending on which of the above is the issue, different modalities may be helpful [time, fillers, laser resurfacing, concealer etc].
Based on the photo, I think your issue is a combination of 1 and 2. Fillers are probably your best option to minimize this, but it will not remove the discoloration, just camouflage it a bit better.