I have very bad dark circles, not just under my eye but around it too. Any tips to lighten it?

It could be caused from stress of lack of sleep I would try and get a good night of restful sleep and see if that helps, If it is stress then try and stress less and see if it helps.

Could be a reaction to some thing applied to the face , I would test it by putting nothing on my face for a week and see if it lightens up some or not.

It could be from dry skin as well in which case a little cream would help that so you could try that out.

Working long hours in front of a computer I have read can cause it as well so limiting screen time.

The only other thing I know of is it could be poor diet and you can eat better.

I am more into home remedies and here are some things I have read that help with dark circles

Almond Oil ( my sister is a model and actually uses this one)
cucumber
tomatoes ( I think juice I would have to re ask my sister)
Rose water
Turmeric
Tea bags
cold compress
lemon juice
coconut oil

Best of luck of you